NATS 1870A: UNDERSTANDING COLOUR (SU 2025) MIDTERM EXAM: FORMAT AND EXPECTATIONS When and Where: • Sunday, June 15th, 9am-12pm (‘Toronto time’) (3 hours) • In eClass, go to the new MIDTERM EXAM section at the top of the course home page. At the start of the exam, you will see these two items: o ‘Midterm Exam Articles and Instructions’file, revealing the 3 new articles to be used for this exam. o ‘Midterm Exam Submission of Answers’link, opening a TurnItIn assignment submission link for you to submit your typed responses file, within the exam time window listed above. • Make sure you have the necessary technology (computer with stable internet connection) available exactly when you need it for this exam. • Late penalty policy: any exams submitted after the indicated deadline will be deducted a late penalty of 1 mark (out of 30) for every 10 minutes past the deadline, within the first hour after the deadline; no further exams will be accepted after 1 hour past the original ending time. Exam Format and Settings: • This exam is based on Lessons 2-12, with all connection points and questions to be made to concepts explicitly covered in these lessons. • You will be presented with 3 (three) different media science news articles to read, each with a suitable word count range (around 800-1,000 words approximately), from sources like https://scitechdaily.com/ and https://phys.org/, published outside of our research project’s period. • For each article, you will then complete a typed response (on your own device) containing 2 connection points and 1 multiple-choice question, as follows: o 2 (two) connection points between the article and our lesson materials (lesson slides and/or readings, over single or multiple different lessons covered this term). Each connection point should: Have a clear title given for the connection point, including the general scientific concept being connected between the article and the lesson (eg: Colour sensitivity ranges of human vision), and a specific reference to the lesson materials (eg: Lesson 3 slides (#19, 21)) Be written fully in your own words! Copying sentences, in part or in full, from the articles themselves and/or lesson materials constitutes plagiarism, as does copying/sharing answers between classmates; this in turn may result in deductions ranging in severity. Using other aides like ChatGPT/Google Translator is prohibited, as it can lead to copied material being selected from a variety of sources, resulting in plagiarized content submitted by the student. Instead, after reading each article and identifying the scientific concepts for your connections, try putting the articles away and writing your connection points completely on your own, with proper English grammar and writing style. Demonstrate meaningful insight into the scientific material presented in the article and covered in the lessons, by explaining clearly how your stated scientific concept in the connection point as first explained in our lesson materials is now also being investigated in the scientific research being reported in the assigned news article. Compare-and-contrast type analysis is a good technique to use here, by first comparing the similarities in the scientific concept (between the lesson materials and news article), and then contrasting any possible differences between them as well, such as new or unexpected or contradicting results discovered in the research compared to the previous knowledge on that topic (as covered in the lessons). Make sure there is adequate discussion of both the news article and textbook readings/lessons in each connection point. Note: if using video documentaries (for Iessons 7 or 11 onIy) for (Iesson materiaI’for your connection point, then you must specify the specific timing in the video itself where your concepts are explained. (For all other lessons, use only the lesson slides for references, and not the recorded lesson videos.) Be between 50-150 words long as a general guide. (Higher grades will be assigned for higher quality of connection points presented, and not simply for meeting the minimum word count.) o 1 (one) multiple-choice question created based on the media article, following the same format as our short assignments (i.e. 4 possible answer options, with correct answer identified as well) . Higher grades will be given to questions more conceptual (than just factual) in their nature. • Once you have completed all your responses, with 6 connection points and 3 multiple-choice questions created in total, you will then submit the Word file to the TurnItIn submission link, within the exam time period. • All students will be expected to maintain full academic integrity in the exam by composing their own original responses, which will in turn be reviewed for any possible plagiarism by the TurnItIn software (for example). Although all students will be reading and responding to the same articles, their responses to them should still nonetheless be individual and unique, just as they would be at an invigilated, paper-based exam on campus. Each student is also expected to complete this exam individually and by themselves. The Senate Policy on Academic Honesty is an affirmation and clarification for members of the University of the general obligation to maintain the highest standards of academic honesty. Any instances of plagiarism and/or other breaches of academic honesty policy may be subject to further investigation and possible consequences as outlined in this policy. • Policy on Generative AI: Students are not permitted to use generative artificial intelligence (AI) in this course. Submitting any work created through the use of generative AI tools wiII be considered a vioIation of York University’s Senate Policy on Academic Honesty. If you do not know whether an online resource or tool can be used in this course, please contact your instructor for guidance. For more information, please review AI Technology & Academic Integrity: Information for Students. Example of a Connection Point: Article: Spectacular bird’s-eye view? Hummingbirds see diverse colors humans can only imagine URL: https://www.sciencedaily.com/releases/2020/06/200615155114.htm Connection Point: Colour sensitivity ranges of human vision; Lesson 3 slides (#19, 21) Both the news article (first paragraph) and Lesson 3 slides (page 19) discuss the three types of main-colour (wavelength) cones in our eyes as the basis of typical human colour vision: red, blue, and green. In Lesson 3, slide 21, these three primary colour sensitivities are represented as the vertices of the (gamut, of aII coIour ranges possibIe for us to perceive from their combinations. The range of spectral colours all in the visible section of the EM spectrum that human eyes are sensitive to are labeIIed with waveIengths on the outer perimeter of the CIE (gamut,. In contrast to our eyes, hummingbirds, eyes have an extra (4th) cone sensitive to UV light, with much shorter wavelengths than our shortest- wavelength blue on the gamut. This in turn would significantly expand the hummingbirds, (gamut of possibIe coIours, perceived compared to ours, creating a more diverse colour vision experience shared by many birds and other vertebrates. Additional possible topics for the second connection point in this article (related to other sections in textbook as well): • Discuss the range of non-spectral colours in human versus hummingbird colour vision Example of a Question Based on the Article: Multiple-Choice Question (Conceptual Type): If humans had a 4th cone sensitive to UV light like the hummingbirds, which of these colours perceived by us would NOT be non-spectral? a) Purple b) UV+orange c) UV+blue d) UV+red Correct answer: c Examples of Past Midterm-Exam Articles: Article 1: Building a Better Bulb: New Prototype LED Lightbulb Emits Less of That Troublesome Blue Light (925 words) https://scitechdaily.com/building-a-better-bulb-new-prototype-led-lightbulb-emits-less-of-that-troublesome-blue-light/ Article 2: Optimal Information About the Invisible: Measuring Objects That You Can’t See (904 words) https://scitechdaily.com/optimal-information-about-the-invisible-measuring-objects-that-you-cant-see/ Article 3:“Surfing”Particles on Alfvén Waves: Physicists Solve a Mystery Surrounding Aurora Borealis (829 words) https://scitechdaily.com/surfing-particles-on-alfven-waves-physicists-solve-a-mystery-surrounding-aurora-borealis/
INFOSYS 110 Digital Systems Semester Two 2023 Exam Case - Sea Forest Seaweed can change the world – that’s what Sea Forest founder and CEO Sam Elsom believes . In fact, after running a successful clothing label for a number of years , Sam packed it all in to grow seaweed, which is the main operation at Sea Forest. Why is Sea Forest growing seaweed? The seaweed cultivated by Sea Forest is called Asparagopsis . It is a red seaweed native to Australian Coastal waters . Sea Forest is the first to cultivate this seaweed at a commercial scale through both marine and land-based aquaculture. The main incentive for growing Asparagopsis is its effectiveness in reducing the production of methane (a greenhouse gas) in ruminant livestock , including cattle and sheep. It is claimed by Sea Forest that “animals whose diets contain 0.2% Sea Forest’s [Asparagopsis] supplement will have methane reductions up to 98%” , according to a recent scientific publication” . This could drastically impact the effects of climate change. What is Sea Forest’s Current Focus? In the early days , Sam focused on perfecting his product. However, the business is now starting its “rapid growth” phase. Because of this , Sam is focusing on three things: 1. Growing as much Asparagopsis as possible, 2. Developing a network of farmers that will pay to use its supplement product, and 3. Growing awareness of the benefits of Sea Forest’s Asparagopsis supplement amongst major meat purchasers including supermarkets and restaurants , so that they may preferentially purchase product that has been fed Sea Forest Asparagopsis supplements . What does Sea Forest Need? To do this , Sam knows that he needs Business Intelligence on every aspect of his business , from the growth rates of Asparagopsis in different environments , to the preferences of potential primary and secondary customers , including livestock farms and the customers who purchase from those farms . 1 The three objectives in the current focus of Sea Forest, as stated in the exam case, were based on Business Intelligence that informs the company about what their potential customers (livestock farm operators , restaurants , and consumers) want. Such Business Intelligence were obtained by careful analysis of various data collected from Sea Forest’s business transactions and market research efforts . a. In one sentence, based on the context of the exam case, suggest what Sea Forest’s Business Intelligence may have informed them about what its potential customers want, which results in Sea Forest’s current operations . (Hint: For example, LUSH operates in their current mode because their Business Intelligence suggest that their potential customers are “committed to ethical buying and are obsessed with the purity of handmade items” .) (2 marks) b. For the Business Intelligence suggested in your answer to part a, suggest TWO transactions where Sea Forest may have obtained the relevant data to generate such information. Also state what relevant data were obtained in EACH transaction. (8 marks) c . For EACH of the two transactions suggested in your answer to part b, suggest a relevant specific TPS that can be used to process the transaction or capture the relevant data. Describe how such data is captured with a specific made-up example. (5 marks) Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. a. Sea Forest's Likely Business Intelligence: b. Transaction 1: Relevant Data: Transaction 2: Relevant Data: c. TPS 1: Description: TPS 2: Description: 2 As SeaForest’s network for farmer customers grows , the company sets up a relational database to replace the existing spreadsheet record of the farmer’s information and the sales transactions . This change allows Sea Forest to address the emerging issues about their “Quality of Data” as the amount of data grows . In class , you were introduced to 6 dimensions of the Quality of Data: a. Suggest TWO such potential Quality of Data dimensions that are likely to be violated by using a spreadsheet to manage a large amount of transactional data. Justify your suggestions with a brief explanation and a specific example. Note that your suggestions must be related to the nature of spreadsheets for this specific purpose. (9 marks) b. For each of the two violations given in your answer to part a, explain how the use of a relational database instead of a spreadsheet can avoid such violations . Support each explanation with a specific example of relational database design (eg. How the data is organised to minimise the specific violation). Note that your answer must be about how relational databases may address the short-comings of spreadsheets for managing large amounts of data, rather than the properties of relational databases that are not related to such short-comings . (6 marks) Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. a. Dimension 1: Justification: Example: Dimension 2: Justification: Example: b. Explanation for Dimension 1: Specific Example: Explanation for Dimension 2: Specific Example: 3 To further improve its supplement product, Sea Forest intends to partner with some of its expert customers to further develop the growing and processing of their Asparagopsis . In class , we have covered three forms of collaborations and four types of collaboration systems . a. Which form of collaboration covered in class is such partnership? Explain your answer. (2 marks) b. Recommend the most suitable type of Collaboration system covered in this course to facilitate such form of collaboration. Explain the reason for your recommendation. Further justify your recommendation with an explanation about why the other three types are not suitable. (8 marks) c . A junior staff at Sea Forest suggested that an Enterprise System (such as the one described in the Red Sneaker example covered in class) is good for facilitating such collaboration. Given the three potential risks of Enterprise Systems covered in this course, discuss why this is not a good suggestion. (5 marks) Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. a. Form. of Collaboration: Explanation: b. Most suitable type of system: Explanation: Less suitable type 1: Explanation: Less suitable type 2: Explanation: Less suitable type 3: Explanation: c. Discussion about risk 1: Discussion about risk 2: Discussion about risk 3: 4 In order to incentivise large meat purchasers and end users to purchase SeaForest’s supplements , Sam is developing a transparent way for all participants in the supply chain to see the methane reductions they’re supporting. By providing QR codes for farmers and packers to include in their documentation and packing, everyone can trace back to the methane reduction impacts of the meat they’re purchasing. They’ll also be able to see a live tracker of the overall methane reduction that SeaForest has made. Provide four ways that SeaForest can use this information to increase their sales . (8 marks) Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. Sales increase 1: Sales increase 2: Sales increase 3: Sales increase 4: 5 Sam has decided to take this idea one step further by allowing end user customers to keep track of the amount of methane they have saved over time by recording their purchasing history. Users will be able to create an account by entering their name and location. The system will then be able to show live leaderboards of methane savings in each location. a. Provide two security issues and one ethical issue which could result from the information provided in this question. (3 marks) b. For each of these issues provide one action that Sam can take to mitigate the risk. ( 12 marks) Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. a. Security consideration 1: Security consideration 2: Ethical consideration: b. Mitigation 1: Mitigation 2: Mitigation 3: 6 Sam has decided to implement the live tracking analysis of methane reduction and has hired a technology consulting team to implement the systems needed to create this . In order to go live, the consulting team will need to create a system that tracks the number of livestock that are being given SeaForest supplements , the amount of methane reduced through their lifespan, and the breakdown of that methane reduction when the animal is prepared into it’s various cuts . It will also need to be able to allow for end users to create their accounts and track their own methane reduction scores . Sam has worked out a budget for this project and hopes to have it completed within six months to align with their planned marketing campaign. The technology consultants have found it more difficult than expected to create a system that tracks the meat all the way to the end user, and have communicated that the project will take longer than expected. a. Explain what impact this will have on each aspect of the project management triangle. (5 marks) b. Outline one action Sam should take as a result, and describe the impact that this action will have on the project management triangle. (5 marks) c . Justify why this is the appropriate action to take. (5 marks) Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. a. Scope: Cost: Time: b. Action that Sam could take in response: Result of the action on the project management triangle: c. Justification of choice in action in (b): 7 Nine months after going live with the project, Sam has been contacted by an eco-terrorism organisation explaining that they have been able to breach SeaForest’s systems and obtain a list of all of the farmers that use their products as well as the amount of methane they’ve reduced. They have threatened to use that information to target other farmers who do not use SeaForest supplements with targetted protests and disruptions . Provide a critical analysis of the four risk management responses available to Sam along with a recommendation. Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. Mitigate: Accept: Transfer: Avoid: Recommendation: 8 Sam is looking to increase efficiencies in the process of growing Asparagopsis . One of the things that results in higher costs is the fact that SeaForest needs to employ people to regularly check on the Asparagopsis to understand water temperature, mineral content and growth rates . a. Provide a recommendation for how Sam could use the Internet of Things to make this process more efficient. (5 marks) b. Explain which category this solution belongs to belongs to. (2 marks) Copy and paste the following answer template onto the answer field. Fill in your answer accordingly. a. Recommendation of how IOT can be used to make this process more efficient: b. Category of IOT:
INFOSYS 110 DIGITAL SYSTEMS Semester One 2023 Brad loves Jeeps and he loves off-roading. Years ago, when his two boys were little, he would take a video camera to record the family camping trips they took together. One day, he decided to post one on YouTube to see whether anyone would watch it. It turned out that people liked his video and so he started posting more. Eight years later, half a million people subscribe to his channel, TRAILRECON, to watch Brad and his family build vehicles, test equipment, and go on overlanding adventures in the backcountry. Along the way, Brad has been able to create a number of income streams: YouTube ad revenue: Brad earns money when viewers watch advertisements that play before, during and after his videos. Sponsorships: because of his large following, vehicle accessory manufactures (for example, rooftop tents, recovery equipment etc.) will pay Brad to showcase their products in his videos. Merchandising: Brad has created a website (trailrecon.com), to sell a number of products from various vehicle accessory manufacturers. Brad will receive a percentage of the profits from any of their products sold on his website. Brad is also looking to create a new income stream by creating a TRAILRECON membership package. This package will allow members to receive weekly news and updates, to receive a discount on all products on the website, to view videos in advance of the general public, and to attend in person meetups and ride along tours. He currently has data on all of his viewers, sponsors and purchasers of his products in an Excel spreadsheet and hopes that he will be able to use this data to target people to become members. This case is based on TRAILRECON and more information can be found on trailrecon.com 1 Question 1 TRAILRECON runs its business using digital systems. It: 1. publishes and sells DIGITAL media; 2. promotes and sells vehicle accessories on a DIGITAL platform; and 3. collects and handles DIGITAL customer information. For each of the three aspects above, suggest one specific example from the case. Describe one non-digital alternative way of doing it, then suggest one advantage and one disadvantage of doing it digitally. (15 marks) Answer this question using the following template. Copy and paste the following template into the answer area to structure your answer: 1. Publishes and sells DIGITAL media One specific example from the case: One non-digital alternative way of doing it: One advantage of doing it digitally: One disadvantage of doing it digitally: 2. Promotes and sells vehicle accessories on a DIGITAL platform One specific example from the case: One non-digital alternative way of doing it: One advantage of doing it digitally: One disadvantage of doing it digitally: 3. Collects and handles DIGITAL customer information One specific example from the case: One non-digital alternative way of doing it: One advantage of doing it digitally: One disadvantage of doing it digitally: 2 Question 2 TRAILRECON is growing rapidly at the moment. They find that their record keeping with Excel spreadsheets is becoming difficult to manage. Suggest two typical issues about the Quality of Data (covered in INFOSYS110) that TRAILRECON may encounter if they carry on keeping their data on spreadsheets only. How may each of these two typical issues be addressed to minimise the resulting problems? Provide detailed suggestions specific to the case in your answer about how such issues can be addressed. (12 marks) Answer this question using the following template. Copy and paste the following template into the answer area to structure your answer: Relevant Quality of Data Issue #1: Detailed Specific Suggestions to Address Such Issue: Relevant Quality of Data Issue #2: Detailed Specific Suggestions to Address Such Issue: 3 Question 3 Brad often showcases products he sells on his website in his videos, and in these videos, he provides direct links to the relevant products he sells for buyers to click on. Brad wants to understand how often viewers of his videos purchase products from his website. 1. What data mining technique could he use to find an answer? (2 marks) 2. What does this data mining technique do? (4 marks) 3. If the data showed that people who purchased tents also purchased chairs, tables and camp lights, what could Brad do to increase revenue? Provide two examples. (10 marks) Answer this question using the following template. Copy and paste the following template into the answer area to structure your answer: 1. Data mining technique: 2. What this data mining technique does: 3. What Brad could do to increase revenue: Example 1: Example 2: 4 Question 4 Brad is putting together a project to create his membership package. In order to go live with this package, Brad will need to do contract developers to create an online portal in his website. This website will allow members to log into and communicate with other members, sign up to member only events, view videos earlier than the public, and access member discounts on products. Brad has worked out a budget for this project and hopes to have it completed within a month. It soon becomes clear that this is going to take longer than expected to complete, and Brad does not want to go live unless all of those requirements are met. 1. Explain what effect this will have on each aspect of the project management triangle (7.5 marks), 2. Outline one action that Brad could take to manage such effects (as suggested in part 1) (2.5 marks), and 3. Explain what output effect that action would have on one aspect of the project management triangle (5 marks). Answer this question using the following template. Copy and paste the following template into the answer area to structure your answer: 1. Effect on aspects of the project management triangle: Aspect 1: Aspect 2: Aspect 3: 2. Action that Brad could take: 3. Output effect on one aspect of the project management triangle: Aspect: Explanation: 5 Question 5 Brad is now nearly ready to launch his TRAILRECON membership. He’s trying to find ways to use the data he has on his viewers, sponsors and purchases of products to target people with marketing for his membership package. Provide one ethical and two security considerations that Brad will need to be aware of in relation to keeping this data and using it to create targeted marketing materials. For each of these considerations, provide a way that Brad can mitigate the risk. (15 marks) Answer this question using the following template. Copy and paste the following template into the answer area to structure your answer: Ethical consideration: Mitigation: Security consideration (1): Mitigation: Security consideration (2): Mitigation: 6 Question 6 TRAILRECON has grown very quickly and that has substantially increased Brad’s workload. As a result, Brad has been looking at ways to make things easier for him. Like many people, he’s been hearing a lot about ChatGPT over the last few months and he’s keen to understand how he might be able to find some practical ways to use ChatGPT to make things easier for him. Provide a practical example of one Brad could use ChatGPT to assist him in each of the following areas. For each area you must provide a practical example, as well as one potential issue you see with each use case. Creating video scripts (5 marks), Creating website content (5marks), Create routes and timelines for his off-roading adventure trips (5 marks). Answer this question using the following template. Copy and paste the following template into the answer area to structure your answer: Creating video scripts example: Potential issue / risk: Creating website content example: Potential issue / risk: Creating routes and timelines for off-roading adventure trips example: Potential issue / risk: 7 Question 7 This question is not direclty based on the exam case. This visualisation is not good. Critically examine the visualisation against Tuft’s Three Design Principles for Data Visualisation. For any principles that are breached, provide a suggestion to improve the visualisation. (12 marks) Answer this question using the following template. Copy and paste the following template into the answer area to structure your answer: Design Principle 1: Suggestion: Design Principle 2: Suggestion: Design Principle 3: Suggestion:
ELEN30009 Electrical Network Analysis and Design Final Examination, Semester 1 2024 Question 1 (20 marks) Consider the second-order circuit shown in Fig. 1. The switch has been closed for a long time, and then it opens at t = 0. Fig. 1. (a) [8 marks] Derive the second-order differential equation that i(t) must satisfy for t ≥ 0. (b) [12 marks] Consider Vs = 24 V and R2 = 20 Ω . We wish to design this circuit to obtain the following inductor current: The only capacitor available is 5 mF. Determine the circuit parameters R1, R3 , and L. Question 2 (25 marks) Consider the circuit shown in Fig. 2 with input vi (t) and output vo (t). Fig. 2. (a) [8 marks] Show that the impulse response of this circuit is given by (b) [14 marks] Use the convolution method to compute the output response when the input is given by vi (t) = 10u(t) — 5u(t — 4) — 5u(t — 8) V (c) [3 marks] Now, consider the area under the impulse response from (a) stays the same but the time constant of the circuit increases to τ = 100 ms. Which output waveform is closer to replicating the input waveform. using h(t) from (a) or the new h(t) with τ = 100 ms? Explain. Question 3 (30 marks) The circuit in Fig. 3a with input vi and output vo shows the interconnection of three op amp stages. Fig. 3. (a) [3 marks] Does this interconnection involve loading? Justify your answer. (b) [11 marks] Show that the overall transfer function of the circuit in Fig. 3 is given by: (c) [8 marks] Draw the Bode magnitude plot of this circuit. (d) [5 marks] Determine the steady-state output voltage of this circuit when vi (t) = 2 cos(500t + 10o) V (e) [3 marks] Can you think of a use for this circuit? Justify your answer. Question 4 (30 marks) A three-way crossover network is used to couple an audio amplifier to speakers. By replacing the amplifier with a voltage source and each speaker with an 8Ω resistor, the approximate equivalent circuit of the three- way crossover network is composed of three circuits, as shown in Fig 4. Crossover networks are used in audio systems to ensure that the proper frequencies are channeled to the appropriate speaker. A woofer is a low-frequency speaker, and a tweeter is a high-frequency speaker. The circuit also includes a mid-range speaker. The combination of all three speakers allows the entire audio range of interest to be reproduced. Fig. 4a. (a) [14 marks] Find the transfer function H(s) = Vo (s)/Vi (s) for each circuit shown in Fig. 4, where the output voltage is taken across each of the three speakers. Discuss the type of filter each of these circuits implements (justify your answer). Using this information, determine which circuit is used with the woofer, tweeter, and midrange speakers, respectively. (b) [3 marks] For the low-pass and high-pass filters, determine the cut-off frequencies of the circuits in Hz. (c) [5 marks] For the band-pass filter, determine the quality factor and bandwidth (in Hz) of the circuit. Based on the calculated quality factor, is the circuit overdamped, underdamped, or critically damped? (d) [8 marks] A fellow student engineer at Unimelb has developed the circuit shown in Fig. 4d. The student argues that the circuit in Fig. 4d can also be used to implement a crossover network with a similar behaviour to the circuit in Fig. 4a. To confirm this statement, determine the behaviour (i.e., filter type) of each of the circuits in Fig. 4d. You must justify your answers for full marks. Fig. 4d. Question 5 (30 marks) (a) [5 marks] Calculate the h parameters for the circuit shown in Fig. 5a. Fig. 5a. (b) [7 marks] Calculate the z parameters for the circuit shown in Fig. 5b. Fig. 5b. (c) [4 marks] The following experimental data has been obtained from dc measurements made on a resistive two-port network. Choose one of the six possible sets of equations for two-port networks and determine the corresponding parameters. (d) [14 marks] The three two-port circuits from items (a), (b) and (c) are interconnected in cascade. The input port of the circuit from (a) is driven by a 5 V dc voltage source in series with an internal resistance of 10 Ω . At the output port of the circuit from (c) is a load resistor ZL that is adjusted until maximum power is delivered to the load. Calculate the maximum power delivered to this load. Question 6 (45 marks) (a) [15 marks] Design a Butterworth band-reject op amp filter with a lower cutoff frequency of 100 Hz and an upper cutoff frequency of 400 Hz. The passband gain of the filter is 0 dB. The filter must be designed with a gain of no more than -20 dB at 180 Hz. Use 39.8 nF capacitors in the high-pass circuit and 10 kΩ resistors in the low-pass circuit. (b) [7 marks] Draw a circuit diagram of the filter designed in (a) and label all the component values. (c) [10 marks] A Melbourne-based company designed the passive RLC filter with an op amp buffer circuit shown in Fig. 6c. The supplier of the inductor is no longer in business and a suitable replacement is not available. You have been asked to design a suitable replacement without inductors. To minimise production changes, your design must use the existing op amp and as many 1 kΩ resistors as possible. Draw the replacement circuit and label all the component values. Hint: determine the behaviour of the circuit and then design a suitable active Butterworth filter replacement. Fig. 6c. (d) [13 marks] The op amp in Fig. 6d has the characteristics described in Table 1, as obtained from the op amp datasheet. Fig. 6d. Table 1 ve supply-2 VOutput swing headroom to neg ASlew rate1 V/ (i) [3 marks] Consider vin (t) = 2 cos(100t) V, Vcc = 12 V and —VEE = —12 V. What is the maximum op-amp gain before saturation occurs? Show your calculations. (ii) [3 marks] Consider Rf = 10 kΩ, determine the effect of the input offset current on the output voltage. (iii) [3 marks] Consider Rf /Rin = 99, determine the effect of the input offset voltage on the output voltage. (iv) [4 marks] Consider vin (t) = sin(2π × 105 t) V and Rf /Rin = 10. Is the output voltage affected by the slew rate specification? If so, what is the impact on the output waveform? Justify your answer.
SC1101 Big Ideas Assessment Task Learning Outcomes Upon completion of this assessment piece, students will be able to: - Demonstrate knowledge of some of the key ideas and inventions in science and technology; - Retrieve, analyse, synthesise and evaluate information from a range of sources; - Convey scientific ideas, arguments and conclusions clearly and coherently through well-developed written and oral communication skills and a variety of media - Reference appropriately in scientific writing Task Description Your task is to write a two-paragraph essay of no more than 350 words, on the scientific invention or discovery that has had the greatest contribution to society. The paragraphs will be written as two linking persuasive paragraphs which incorporate scientific writing conventions. The purpose of the exercise is for you to demonstrate your ability to assemble relevant scientific facts and concepts and then express them in a logical, condensed and coherent composition, using appropriate and correct scientific language, English expression, grammar and punctuation. “What scientific discovery or invention has had the greatest impact on society” Format of Assessment - PARAGRAPHS – This assignment is a 2-paragraph essay. The main text should appear as two physically distinct paragraphs. No more, no less. - WORD LIMIT – The limit for this Paragraph assignment is 350 words. Any extra word will result in a deduction. The set word limit: - Does NOT include the Title, student name and JCU student number - Does NOT include the References list at the end of the page - DOES include the in-text references/citations. - FORMAT – This assignment must be typed with a line spacing of 1.5. Fonts prefered are Times New Romam, Arial or Calibri. Your assessment MUST be submitted as a Word file. NOT a PDF or a link to a share file. - REFERENCES FINDING REFERENCES- You need to find 5-10 references from reliable and credible sources. Within each of your references, you will need to highlight the sentence or section you are referencing in each source. Then merge all of your highlighted references into one document and upload that into Learn JCU as one combined file. Make sure to include the entire reference not just the page with the section you have highlighted! Further notes on what to include in your merged references document for different types of references: · Journals-the entire journal article · Books-a copy of ANY chapters you have used · Website- website address AND a screenshot/copy of all text from the whole page of the website USING REFERENCES- Your paragraph must contain 5-10 appropriately cited references. References used must come from reliable and credible sources. Only the APA referencing style. is accepted. APA version 7. Each reference should include both an in-text citation and full reference list after your final paragraph. Reference List should be in alphabetical order. - Check CONTENT, GRAMMAR, SPELLING and WRITING STYLE . All these elements are relevant and will be evaluated in your work. - PLAGIARISM & BAD REFERENCING – Plagiarism is NOT tolerated. To avoid risk of unintentional plagiarism ensure that all statements with information that is not your original work/idea are appropriately referenced, both in the text and in the reference list. SafeAssign is an excellent tool to assist you in avoiding unintentional plagiarism. - SAFE ASSIGN DRAFT CHECKING – Remember to run your final draft of your paragraph through SafeAssign before your final submission so you can check the Originality Report and see if there is any section that needs to be modified or appropriately referenced to avoid risk of unintentional plagiarism. SafeAssign is located in the assessment folder right next to your assessment submission folder for this assignment. Safe assign MAY take a few hours to return a result to you as it compares your assessment with other submissions and online resources. If you wanting to use this resource to check BEFORE your real submission, don’t leave this to the last minute. Assessment Submission - SUBMISSION– You will be uploading 2 files. Part 1 is a single PDF or word file of all of your references combined. Part 2- Is an electronic copy preferably in Word (but it cannot be a PDF or link) of your Big Ideas assignment. Remember to title your files before uploading: Part 1: References for Assessment: SC1101_A1_LASTNAME_FIRSTNAME_REFERENCES Part 2: Your Big Ideas Assessment: SC1101_A1_LASTNAME_FIRSTNAME LATE SUBMISSION – Penalties apply for late submissions: -0.5points will be deducted from the final grade for every day (24hr) the assessment is overdue, including weekends. Example 1: Student 1 has submitted their work 3 minutes past when the assessment is due. Their overall grade for the paragraph would have amounted to 6.5/10 CREDIT, however, considering their late submission ( 0.5points x 1day) their final grade is actually 6/10 PASS. Example 2: Student 2 has submitted their work which was due at 4pm on Friday, on following Wednesday morning at 11 am. Their overall grade for the paragraph would have amounted to 7/10 CREDIT, however, considering their late submission ( 0.5points x 5days, including days over the weekend = -2.5pts) their final grade is actually 4.5/10=FAIL
INFOSYS 110 Digital Systems Semester One 2024 Exam Case The candle making industry is set to eclipse US $10 billion in global sales by 2032, and so after a few months making candles for her family and friends, Ashley decided to see if she could start an online business to supplement her income. Given the plethora of cheap candles available online through sources like Amazon, Ashley decided to start by making hand crafted candles with premium materials. Her first few batches were very much trial and error, but soon, she was making consistently beautiful candles that had a lovely smell, even wick and wax burn, and good longevity. She started her business venture by setting up an online store using Shopify and things escalated quickly from there, with her candles quickly gaining popularity. Ashley had to quickly learn how to run the “business” side of things (including accounting and employing staff), but it was never her strength – she preferred to spend her time researching new ingredients and flavours. To help her research new flavours, her customers are prompted to fill out a questionnaire each time they buy a product, and this gives Ashley information about who is buying her products, and why they like them. Now, two years after her website went live, Ashely is looking at moving her business out of her double garage and into an industrial warehouse. This will allow her to employ more staff, manufacture more inventory, and spend more time on researching new variants. However, she will also need to increase her revenue, and that means increasing sales. Ashley has three strategies for increasing sales: 1. To start advertising on social media platforms, 2. To become a supplier of big box stores like Woolworths, PAK’nSAVE, and Chemist Warehouse, and 3. To enter into partnerships with influencers. Question 1 As for any business these days, the success of Ashley’s candle business relies heavily on its Competitive Advantage, which is based on Business Intelligence. a. Based on the exam case, describe Ashley’s competitive advantage and suggest why it can give her a competitive edge. (4 marks) b. Suggest one example of a DSS that Ashley may use and describe one type of analysis using such DSS that may generate the business intelligence that enables Ashley’s competitive advantage. Give an example of the relevant business intelligence and describe how the analysis can generate such information. (10 marks) c. Ashley needs to collect some data in order to use the DSS to do the analysis. Suggest two forms of data required for such purposes, and two examples of TPSs that can be used to collect such data. (6 marks) You must answer this question using the following template. Copy and paste this template into the answer area and insert your answer. a. Ashley’s competitive advantage: Why it can give Ashley a competitive edge: b. DSS example: Analysis example: Business intelligence example: How the analysis can generate such information: c. Relevant data 1: Relevant data 2: TPS example 1: TPS example 2: Question 2 Now that Ashley’s candle business is into its second year, and that it has undergone major expansions (as described in the case). Ashley is considering about implementing an Enterprise System (ERP) for her operations. a. In no more than three sentences, describe specifically one advantage for Ashley’s business if an Enterprise System is implemented. (5 marks) b. In no more than three sentences, describe specifically one disadvantage for Ashley’s business if an Enterprise System is implemented. (5 marks) c. In your opinion, should Ashley’s business implement an Enterprise System? Justify your answer with no more than three sentences. (5 marks) You must answer this question using the following template. Copy and paste this template into the answer area and insert your answer. a. One advantage for Ashley’s business: b. One disadvantage for Ashley’s business: c. Yes/No: Justification: Question 3 Ashely is looking to understand who her social media advertisements should be targeted at, and she’s hoping that her past sales data can provide an insight into this. To save time and costs, she’s hoping to run different campaigns, each targeted at a different group of people. a. What data mining technique would help Ashely understand how many campaigns she should run, and who they should be targeted at? (1 mark) b. Explain how the data mining technique works and explain how it can help Ashley. (5 marks) c. If the results of this data mining technique show that a significant portion of Ashley’s customers are purchasing her products as gifts, what is one action Ashley could take to increase sales revenue, and how would that action contribute to the increase in revenue? (4 marks) You must answer this question using the following template. Copy and paste this template into the answer area and insert your answer. a. A helpful data mining technique: b. How the technique works: How it can help Ashley: c. One action that Ashley could take: How it will contribute to the increase in revenue: Question 4 Ashley has drafted template partnership contracts to be signed by the influencers she is hoping to work with. These contracts state that the influencers will need to provide Ashley with details of all viewers who express interest in Ashley’s products, including their social media names, and any other data they collect. a. Provide and describe one ethical and two security consideration that Ashley will need to be aware of when finalizing these contracts. Support your answers with case specific justifications. (6 marks) b. For each of these considerations, provide an analysis of actions of the risk management responses we discussed in class (described in the context of the case. Generic descriptions will receive no marks), and provide a recommended action with reason. (18 marks) You must answer this question using the following template. Copy and paste this template into the answer area and insert your answer. a. One Ethical Consideration: Justification: Security Consideration 1: Justification: Security Consideration 2: Justification: b. Risk management responses for the Ethical Consideration · Mitigate: · Accept: · Transfer: · Avoid: Recommended action: Reason: Risk management responses for Security Consideration 1 · Mitigate: · Accept: · Transfer: · Avoid: Recommended action: Reason: Risk management responses for Security Consideration 2 · Mitigate: · Accept: · Transfer: · Avoid: Recommended action: Reason: Question 5 One of the influencers Ashley partners with has contacted her, asking for an increase in her monthly fee. As evidence to support this request, she’s provided Ashley with this visualization to show the impact her social media page has on Ashley’s products. Provide Ashley with two critiques of this visualisation that can help her respond to the request (8 marks). For each critique, explain which of Tufte’s principles is violated (2 mark), and provide a suggestion for how this visualization should be changed (6 marks). You must answer this question using the following template. Copy and paste this template into the answer area and insert your answer. Critique 1: Violated principle: Suggestion to change visualization: Critique 2: Violated principle: Suggestion to change visualization: Question 6 Answer the parts in this question based on the following Python code: a. Using natural language, in one sentence, describe what this code does. (4 marks) b. Using natural language, describe what line 11 “print(f"Roll {rolls}: You rolled a {result}")” does and provide a made up example of its output in the context of the program. (8 marks) c. Using natural language, in one sentence, describe what the final line “play_game()” does. (3 marks) You must answer this question using the following template. Copy and paste this template into the answer area and insert your answer. a. What this code does: b. Description of the line of code: Example output: c. Description of the line of code:
MATH2FM3 Problem #1: A 3 year bond with semiannual coupons of 11% has a yield of 18.12%. You are to use Excel's "SumProductl function to compute the duration of this bond. Given two ranges of values, "SumProduct" computes their dot product. Create a table as shown, with entries appropriate to your bond, replacing the question marks with appropriate formulas. In a single cell, use the functions "SumProduct" and "Sum" to compute the duration of this bond using only the cells shown above. (a) What is the duration of this bond? (b) What formula using the functions SumProduct and Sum (and using 37 characters or less) calculates this duration? Problem #2: Excel's Solver utility can also find an optimum solution involving more than one variable. We will use Solver to find the best fit of a straight line yield curve for some bond prices (more information on Solver is available in the previous assignment, or in the online tutorial). You are to calibrate a straight line yield curve where y(t) = yo+mt by finding appropriate values for yo and m. The value y(t) is the semiannually compounding bond yield, or IRR, for a bond of maturity t. The yield curve is to be the best straight-line fit for the following four bonds: Bond 1 has face value $100 and a term of 1 year with semiannual coupons of 5% and a price of $101.13. Bond 2 has face value $100 and a term of 1.5 year with semiannual coupons of 8% and a price of $104.19. Bond 3 has face value $100 and a term of 2 year with a semiannual coupon of 6% and a price of $100.95. Bond 4 has face value $100 and a term of 5 year with a semiannual coupon of 3% and a price of $82.47. Create a spreadsheet with headings similar to the following: In column G, you are to price the bond based on the yield from column F. Column H contains the actual price of the bond. Column I is the difference between the two prices, squared. In cell I13, we have the sum of thel differences squared, and it is this value that we seek to minimize. Use Excel's Solver add-in to simultaneously solve for yo and m to minimize the sum of the differences squared. (a) What is the value for yo found by Solver? (b) What is the value for m found by Solver? Problem #3: In a previous assignment, Excel wrote a Macro for you by recording your actions. The language the Macro was written in was Visual Basic, or VBA. You can use VBA to program functions or subroutines for yourself. In this exercise you are to write an interpolation function in VBA. You will need to have the "Developer" tab appearing on your ribbon. If it's not there, find "Options" under File or Home, click on "Customize Ribbon" and activate "Developer". Make a yield curve by interpolating and extrapolating from four given terms and yields. Create a table of values on a spreadsheet as shown below, but with the following terms and yields: Term Yield 1 4.00% 1.5 6.50% 3 3.50% 5 7.50% Create a straight-line interpolation function in VBA called, FInterp(x, xarray, yarray), that takes as input an array of x values, an array of their matching y values, and the x value for which you want it to interpolate/extrapolate a y value. Instructions for doing this are here. Create a new table with column headings Term Interpolated Vlookup true Vlookup false Under "Term", create a column of terms running from O to 6.0 by increments of 0.2. In the "Interpolated" column, for each term, call your FInterp to interpolate/extrapolate the yield for that term (If your sheet appears like the one above, the xarray input for the interpolator is $B$5:$B$8, while the yarray is $C$5:$C$8). For comparison, also find what the "vlookup" function produces. In the column beside your "Interpolated" column, use vlookup on the table $B$5:$C$8 for each term, with the optional 4th argument, "Range lookup", set to "TRUE" to have vlookup provide the closest match. In the last column, again use vlookup, but with "Range_lookup" set to "FALSE" so that it returns #N/A if there is no exact match. (note: with vlookup set to false, vlookup may return #N/A even for terms of 3 and 5. The failure to find a match is due to unseen numerical errors somewhere around the 16th decimal place of the value in the "Term" column. Your solution will be accepted even with the #N/As). (a) What value does your interpolator return for a term of 2.0? (b) What value does your interpolator return for a term of 0.6? Problem #4: Referring to Problem #3 above, select all the data in all four columns of the table that you created, and "Insert" a Scatter Chart plotting all three columns of results against terms from O to 6. For the plot, select the type that indicates each of the points, and connects those with straight lines. Take a screen shot with your graph clearly visible. Paste it into an application (like Paint), and save it as a (.png) file. Upload your screenshot here: Problem #5: A zero coupon bond of term 3 years has a continuously compounding yield of 2.17%. A zero coupon bond of term 5 years has a continuously compounding yield of 3.55%. Use Excel to compute the two year quarterly compounding rate 3 years forward.
Department of Electrical and Electronic Engineering ELEN30009 Electrical Network Analysis and Design Semester 2 Assessment, 2022 Question 1 (4+10 = 14 marks) Consider the second-order circuit shown in Fig. 1. The switch has been in the closed position for a long time, and then it opens at t = 0. Fig. 1. (a) Determine the initial conditions (b) Find the expressions of v1 (t) and v2 (t) for t ≥ 0 using the time-domain method, i.e., you MAY NOT use Laplace transform. for this question. Question 2 (2+8+6 = 16 marks) Consider the circuit shown in Fig. 2 with a current source input is (t) and the output io (t) as the current through the inductor. Fig. 2. (a) Show that the impulse response of the circuit is A. (b) Use the convolution integral to compute the output response when the input is given by: (c) Now, consider is (t) = cos(10t)u(t) A. Derive the expressions for Io (s) and io (t). Question 3 (4+3+6+2+5 = 20 marks) Consider the circuit shown in Fig. 3 with input vi (t) and output vo (t). Fig. 3. (a) Show that the frequency response of this circuit can be written as where w1 = 1/(R1c1) and w2 = 1/(R2c2). (b) Using R1 = 2 kΩ, design this circuit to provide a voltage gain of 40 dB in the passband with a low- frequency 3-dB point at 200 Hz and a high-frequency 3-dB point at 200 kHz. (c) Plot the Bode magnitude and phase response of this filter. (d) A sinusoidal input vi (t) = A cos(wt + φ) is applied to this filter with the following parameters: • Magnitude: 2 V. • Frequency: 10 kHz. • Phase: 45。. Determine the steady-state output voltage of the filter. (e) Design an active cascaded broadband bandpass filter to achieve the same specifications in (b). Use 0.4 μF capacitors. Draw the circuit diagram of your final design and label all component values. Question 4 (6+4+2=12 Marks) You are in the process of completing a circuit for on-farm sensing application that will need to amplify signals in the frequency range of 0-80 MHz. However, when you were testing this circuit, you realise that the VHF radio transmitting tower nearby is causing a strong interfering signal around 95-105 MHz and saturates your amplifiers in the circuit. You are now required to complete the design of a passive band-reject filter of the form shown in Fig. 4 with following specifications: • Centre frequency = 100MHz • Bandwidth = 10 MHz • You may assume that the antenna and the amplifier circuits will not load this filter circuits as you plan to use buffer amplifiers to ensure this is the case. Fig. 4. (a) Obtain the transfer function H(s) that relates output voltage Vo (s) to Vi (s) of the band-reject filter form. shown in Fig. 4. Identify the parts of the transfer function that determines the centre frequency and the bandwidth of the filter. (b) To set the centre frequency at 100 MHz, select first a value for inductance (L) from the available collection of 1μH, 100 μH, 1 mH, and 100 mH and then calculate the capacitance (c). (c) Determine the value of the resistance (R) to achieve the required bandwidth of 10 MHz. Question 5 (2+4+2+6+4=18 Marks) Two engineers are attempting to fix a circuit attached to a sensor device. After closely examining the circuit elements and their interconnections, they come up with an equivalent circuit shown in Fig. 5 and now they are trying to understand the function of this circuit. You are required to help them with the analysis. The circuit has been in the unpowered state for a long time and thus can be assumed to be free from any stored charge. (a) Assuming the operational amplifier is ideal, determine the current through the positive and the negative terminal of the operational amplifier. (b) By applying suitable circuit laws, derive the expression for describing the time domain description of the output voltage vo (t) as a function of vi (t), assuming there are no initial conditions, i.e., vi (t = 0) = 0 and vo (t = 0) = 0. (c) Based on the expression obtained in (b), describe the function of the circuit. (d) You realise that the circuit is built with a real operational amplifier with a finite gain A. Derive an expression for the output voltage Vo (s) in frequency domain by taking this into account. (e) Identify two imperfections or limitations of real operational amplifiers and discuss how they will impact the function of the circuit. Question 6 (4+6+4+3+3=20 Marks) You are working with a circuit shown in Fig. 6b where two identical two-port circuits (as shown in Fig. 6a) are used to connect the signal source Vs = 80∠0。mV with a source resistance fRs = 50Ω to a load with resistance of RL = 50 Ω. You have no knowledge of internal makeup of the circuit. However, it is known to have no frequency dependence over the frequency range of interest. To model the two-port circuit shown in Fig. 6a using its A-matrix, the following two sets of measurements are made to help you with the determination of the circuit’s a-parameters. The results are summarised below. Fig. 6. (a) Using the measurements, derive the a-parameters of the two-port circuit. (b) Using the a-parameters obtained in (a) for the two-port circuit of Fig 6a, determine equivalent a- parameters for the combination of two identical two port circuits. (c) Determine the output voltage Vo across the load RL produced by the input source Vs = 80∠0。mV. (d) Determine the power delivered to the load. (e) Determine the power delivered by the source.
LEVEL 1 MATHS AT LONG BAY COLLEGE Credits: 5 Instructions and information: 1. Before undertaking this assessment, you must read and sign the authenticity statement via the link here: Authenticity Statement 2. Read through the information before starting your assignment. 3. Follow your teacher's instructions for how to submit your assessment (this could be via Assignments in teams, in One Note or printed out and handed in). 4. This task sheet briefly outlines what you should include in your report. You should access your class notes and your class One Note or Content Library for additional resources. 5. You may conduct contextual research online (within the authenticity guidelines) to support your investigation. 6. You may use an appropriate graphing program or website to set up your data displays. 7. You may work on your assessment both in the allocated class time and outside of class time. 8. Your teacher will tell you when your first draft is due for Achieved checking and basic feedback. 9. The due date for the final draft of your task is 3:30pm on Friday 27 June 2025. 10. Present your investigation in a written report of up to 1000 words. In this Assessment Activity, you will use the Long Bay College results from our participation in the Census At School Tatauranga Ki Te Kura to investigate information that has been collected by students in year 11 Mathematics at Long Bay College, about themselves, in Aotearoa New Zealand. You will follow a statistical enquiry process and have the option to: A. Complete a COMPARISON report by comparing a single variable between two groups OR B. Complete a RELATIONSHIP report by determining a relationship between two variables for a single group. PREAPPROVED QUESTIONS You may select from one of the four questions below or your own preferred question. Comparison Questions: 1. I wonder if the distance (in cm) jumped by students who had a target line tends to be greater than the distance (in cm) jumped by students without a target line for level 1 Mathematics students at Long Bay College. 2. I wonder if the time taken (in minutes) to travel to school by bus for level 1 Mathematics students at Long Bay College tends to be greater than the time taken (in minutes) to travel to school by car for level 1 Mathematics students at Long Bay College. Relationship Questions: 1. I wonder if there is a relationship between the height (in cm) of level 1 Mathematics students at Long Bay College and the left foot length (in cm) of level 1 Mathematics students at Long Bay College. 2. I wonder if there is a relationship between the right foot length (in cm) of level 1 Mathematics students at Long Bay College and the standing jump distance (in cm) for level 1 Mathematics students at Long Bay College. Own Comparison or Relationship Question: Should you prefer to investigative a statistical question of your own choosing, please discuss your investigative question with your teacher and have it approved before starting your report. Step 1: Exploring a purpose Use the level 1 Mathematics Students at Long Bay College Data Set from the Census At School survey to explore the data. As part of your exploration, you should identify the purpose of your investigation and consider the benefits of any enquiry process you complete. What might you expect to find in your investigation? How useful will the findings be and how widely could they be applied? complete for this Assessment Activity. If you do not opt for one of the preapproved questions above, your After your exploration, decide on the specific comparison or relationship investigation you would like to kaiako will look at your chosen investigation and confirm with you the formal investigative question or statement that you will use in steps 2-4. They will also help you to identify the population you are working with. The population for this assessment is "level 1 Mathematics students at Long Bay College." Step 2: Planning the investigation Identify the variables of the data that you have sourced and check if they meet the requirements of your investigative question or statement. Ensure that you record your population. Describe the data collection process that was used to source data for your investigation. This may include identifying and explaining different sources of variation that need to be controlled in the original process of collecting this data and explaining the effect of controlling the variation. Step 3: Sourcing and preparing data Source appropriate data for your investigation. Clean your data where necessary and prepare it for analysis. Step 4: Exploring, analysing, and forming conclusions about the data Using applications such as NZGrapher select and use appropriate visualisations and suitable measures. What do you notice as you explore the visualisations? Link your comments about features to the context of your investigation. Now that you have explored the data, explain what you have learned that is relevant to the purpose of your enquiry. If your investigation is based on a relationship between two variables, use your findings to make a useful prediction. Discuss any choices you made and the usefulness of any results. Make informal inferences or generalisations using your data, discuss sampling variability, and reflect on the statistical enquiry process. Remember to always link back to the investigation purpose. How to present your learning Written report- up to 1000 words maximum. Student resources In One Note, you have access to the full set of data and the census questions.
MATH375: Tutorial 4 1. Consider the following nonlinear stochastic differential equation (called the Cox-Ingersoll-Ross (CIR) equation): where a, b, σ, are positive constants. Show that its solution (X(t),t ≥ 0) satisfies the mean-reverting property. [Hint: Integrate both sides of the equation from 0 to t, take the expected value of both sides, and solve the resulting equation for E[X(t)].] 2. Consider the following market of two assets: Let us introduce a new asset in this market with price Y (t) satisfying: dY (t) = uB (t)dB(t) + uS (t)dS(t), t ≥ 0, for some F(t)-adapted processes ((uB (t), uS (t)),t ≥ 0) such that this equation has a unique solution. Show that this enlarged market of three assets does not admit arbitrage opportunities. 3. Consider the following market of two assets: where r, µ1, σ1, are given positive constants. Let us introduce a new asset in this market with price process Y (t) satisfying for some positive constants µ2, σ2. Show that in this market of three assets, if there is an arbitrage opportunity.
Adequate Sets of Connectives Adequate Sets of Connectives Consider the connectives ¬, →, ∧, ∨, and ↔. We have seen that ∧, ∨, and ↔ can all be expressed in terms of ¬ and →, so we only use ¬ and → in our official definition of formula. Could we have used other connectives in the definition? Definition A set C of connectives is adequate if every formula is logically equivalent to a formula using only connectives from C. Example {¬, ∨} is an adequate set of connectives. By definition, {¬, →} is adequate. To see that {¬, ∨} is adequate, it suffices to show that → can be expressed in terms of ¬ and ∨. Now for any formulas ϕ and ψ, (ϕ → ψ) (¬ϕ ∨ ψ). Thus, {¬, ∨} is adequate. Logical Consequence and Tautologies Logical Consequence — Validity Revisited Definition Let Γ be a (possibly empty, possibly infinite, possibly finite) set of propositional formulas, and let ϕ be a propositional formula. We write Γ |= ϕ and say ϕ is a logical consequence of Γ if for every truth assignment e, if e is such that e(γ) = T for all γ ∈ Γ, then e(ϕ) = T. Note that for finitely many formulas {ϕ1, . . . , ϕn} and a formula ϕ, we had already defined {ϕ1, . . . , ϕn} |= ϕ with this same definition. Question Which of the following formulas are tautologies? 1. ((P ∧ Q) → P) 2. (P ↔ ¬P) 3. ((P ∧ ¬P) → Q) 4. P Disjunctive Normal Form Relaxed Notation You can check that for any formulas ϕ, ψ, and χ, we have ((ϕ ∧ ψ) ∧ χ) (ϕ ∧ (ψ ∧ χ)) For this reason, in situations when we are concerned with the formulas only up to truth equivalence, we will often write (ϕ ∧ ψ ∧ χ) as an abbreviation for ((ϕ ∧ ψ) ∧ χ). More generally, for formulas ϕ1, . . . , ϕn, (ϕ1 ∧ . . . ∧ ϕn) abbreviates (. . . ((ϕ1 ∧ ϕ2) ∧ ϕ3) ∧ . . . ∧ ϕn). Since we also have ((ϕ ∨ ψ) ∨ χ) (ϕ ∨ (ψ ∨ χ)) as well, we make the analogous abbreviations with ∨ in place of ∧. Definition For formulas ϕ and ψ, we refer to (ϕ ∧ ψ) as the conjunct of ϕ and ψ, and we refer to (ϕ ∨ ψ) as the disjunct of ϕ and ψ. Disjunctive Normal Form Up to truth equivalence, propositional formulas are completely described by their truth tables. However, as we’ve seen, truth tables for formulas in many variables are rather large. The disjunctive normal form. (DNF) of a formula will be a formula that is truth equivalent to the original, but it will tell us exactly the rows of the truth table on which the formula is true. Question Which of the following formulas are in disjunctive normal form, over all variables occurring in the formula? 1. ((P ∧ ¬Q ∧ R) ∨ (¬P ∧ Q ∧ ¬R)) 2. ((P ∧ ¬Q) ∨ (P ∧ R) ∨ (¬P ∧ Q)) 3. ((P ∧ Q) ∨ (P ∧ ¬Q) ∨ (¬P ∧ Q) ∨ (P ∧ Q)) Uniqueness of the Disjunctive Normal Form Disjunctive Normal Form Theorem For every propositional formula ϕ with propositional variables among P1, . . . , Pn, there is a formula ψ with propositional variables P1, . . . , Pn that is truth equivalent to ϕ and is in disjunctive normal form. Moreover, ψ is unique up to rearrangement of the DNF constituents. Definition If ψ ϕ and ψ is in disjunctive normal form, we call ψ the disjunctive normal form. of ϕ.
Economics 201 Microeconomics Tutorial 9 Question 1: Consider the following two player game. The first number in each cell refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Players move simultaneously. Which of the following statements is INCORRECT? Player #1 Player #2 Left Right Top 7, 7 0, 4 Bottom 4, 0 4, 4 (a) This game has two Nash equilibria: {Top, Left} and {Bottom, Right}. (b) {Top, Left} is the payoff dominant outcome. (c) If players are excessively risk-averse then we could see a relatively high proportion of {Bottom, Right} outcome. (d) {Bottom, Right} is the payoff dominant outcome. Question 2: Consider the following two player game. The first number in each cell refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Players move simultaneously. Which of the following statements is CORRECT? Player #1 Player #2 Left Right Top 8, 14 8, 8 Bottom 10, 6 12, 8 (a) Player #1 has a dominant strategy, Bottom; there is a unique Nash Equilibrium in this game and that is {Bottom, Right}. (b) Player #2 has a dominant strategy, Right; there is a unique Nash Equilibrium in this game and that is {Bottom, Right}. (c) Player #1 has a dominant strategy, Bottom; player #2 has a dominant strategy, Right; there is a unique Nash Equilibrium in this game and that is {Bottom, Right}. (d) There are two Nash equilibria in this game – {Top, Right} and {Bottom, Left}. Question 3: Consider the following two player game. The first number in each cell refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Players move simultaneously. Which of the following statements is INCORRECT? Player #1 Player #2 Left Right Top 5, 3 0, 0 Bottom 0, 0 3, 5 (a) There are two equilibria in this game: {Top, Left} and {Bottom, Right}. (b) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 5/8 and Bottom with probability 3/8; Player 2 should play Left with probability 3/8 and Right with probability 5/8. (c) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 3/5 and Bottom with probability 2/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5. (d) Players would prefer to coordinate to one of the equilibria, either {Top, Left} or {Bottom, Right} rather than end up at either {Top, Right} or {Bottom, Left}. Question 4: Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Suppose the two players move simultaneously (at the same time). Which one of the following statements is correct? Player #1 Player #2 Left Right Top 7, 7 0, 4 Bottom 4, 0 4, 4 (a) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 4/7 and Bottom with probability 3/7; Player 2 should play Left with probability 4/7 and Right with probability 3/7. (b) There is a unique dominant strategy Nash equilibrium at {Bottom, Right} (c) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 2/5 and Bottom with probability 3/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5. (d) In the mixed strategy equilibrium of this game, both players should randomize over the strategies with probability ½ and ½. Question 5: Consider the following two-player game with players moving sequentially. Player 1 moves first and can choose to either “Take” or “Pass”. If Player 1 chooses “Take” then the game ends immediately and Player 1 gets $8 and Player 2 gets $12. If Player 1 chooses “Pass” then Player 2 gets to move. Player 2 can choose “Take” or “Pass”. If Player 2 chooses “Take” then the game ends immediately. Player 1 gets $10 and Player 2 gets $15. If Player 2 chooses “Pass” then Player 1 gets to move again. Player 1 can choose “Take” or “Pass”. In either case the game ends after Player 1’s move. If Player 1 chooses “Take” then Player 1 gets $20 and Player 2 gets $10. If Player 1 chooses “Pass” then Player 1 gets $10 and Player 2 gets $20. Which of the following statements is CORRECT? (a) Player 1 should choose to “Take” at the very first opportunity to move. (b) Player 2 should choose to “Take” at the very first (and really only) opportunity to move. (c) Player 1 should choose to “Pass” in his/her second opportunity to move. (d) Player 2 should choose to “Pass” at the very first (and really only) opportunity to move. Question 6: Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. If Player 1 moves first and player 2 follows, then using the principle of backward induction the subgame perfect equilibrium of this game is: Player #1 Player #2 Left Right Top 8, 4 2, 2 Bottom 2, 2 4, 8 (a) Top, Left. (b) Top, Right. (c) Bottom, Left. (d) Bottom, Right. How would the outcome of the game change if Player #2 moved first?
Assignment 1: Make an Offer on a Home Case Study: You and your spouse, both in your 40s, work at the University of Washington at the Seattle campus. You have two children. Your annual household income is $280,000 (after tax income of $210,000). Non-housing expenses per month are approximately $8,000, which includes $2,600 of reoccurring debt. You have $120,000 in savings for closing costs and a downpayment. Your aim is to allocate up to 3% of the purchase price for closing costs and use the rest for the downpayment. You plan to stay in the home for at least five years. Your credit score is 790. Search for a home in the Seattle area that fits within your budget and is located within commuting distance of your place of work. Address of Property (2 points) Please provide the full address of the property. Web Link of Property Listing (3 points) Please provide the link to the website where you found the property. For example, this may be the listing on Zillow, Redfin, or Realtor.com. Affordability Analysis (15 points) Describe the method(s) you used to determine how much house you can afford. This can be any of the methods from the readings, online affordability calculators, or other methods you have identified. It is recommended you use more than one method to determine an affordability range. Offer Price (15 points) Determine a price that you are going to offer for the home. Describe how you decided on the offer price. What market information did you use and what other factors did you consider in the price determination? Home Selection (10 points) Describe why you selected this home and what factors you considered when searching for a home for your family. Discuss the tradeoffs you had to make in order to find a house that fit your budget while still meeting your needs. Earnest Money Deposit (5 points) Determine an amount for the earnest money deposit. Describe why you selected that amount and the benefit or consequences of offering more or less for the earnest money.
MATH375: Tutorial 3 1. Let (F W (t),t ≥ 0) by a filtration for Brownian motion (W (t),t ≥ 0). Show that the following processes are martingales relative to this filtration: 2. Using Itˆo’s formula, show that the following processes are martingales with respect to the natural filtration (F W (t),t ≥ 0) of Brownian motion, and find their representation: 3. Consider the stochastic differential equation: for some given constants a, b, σ. Find its solution (X(t),t ≥ 0). [Hint: Consider the ordinary differential equation i.e. y(t) = e −at is a known function. Apply Itˆo’s formula to X(t)y(t) so that the unknown X(t) on the right-hand side of the stochastic differential equation is eliminated.]
ACF5130 Financial statement analysis and business valuation Week 7: Financial Analysis Discussion Question 1: Analysing Woolworths’ ROE ROE data from Sandip’s Woolworths Valuation Discussion Questions: ● How would you interpret Woolworths’ performance? ● Discuss some advantages of time-series analysis of financial ratios. ● Discuss some limitations of time-series analysis of financial ratios. Discussion Question 2: Analysing Woolworths’ ROE Competitor ROE data from DatAnalysis Premium; Woolworths ROE from Sandip’s Woolworths Valuation Discussion Questions: ● How would you interpret Woolworths’ performance, relative to that of competitors? ● Discuss some advantages of cross-sectional ratio analysis. ● Discuss some limitations of cross-sectional analysis. Discussion Question 3: Advanced DuPont Analysis Imagine you're conducting a financial analysis of two technology sector companies, Company A and Company B, both of which have similar business models and revenue streams but divergent capital structure strategies. Upon reviewing their financial statements, you observe that both companies exhibit a return on equity (ROE) lower than their respective returns on net operating assets (RNOA). Further investigation reveals that while Company A's net borrowing costs (NBC) exceed its RNOA, Company B, however, does not face this issue. Considering the Advanced DuPont decomposition of ROE: ROE = RNOA + SPREAD*FLLEV Explain why Company B's ROE is lower than its RNOA, despite its NBC being less than RNOA. Both companies maintain positive equity. Evaluate the sustainability of the capital structures of Companies A and B based on your analysis. Additionally, propose any strategic adjustments you would recommend to the management of each company. Discussion Question 4: Advanced DuPont Analysis The following exhibits are the partial financial statements of ABC Ltd for the years ended 31 December 2022 and 2023 respectively. Discussion Question 4: Advanced DuPont Analysis The following exhibits are the partial financial statements of ABC Ltd for the years ended 31 December 2022 and 2023 respectively. Supply the missing numbers and calculate the ROE. Show the Reformulated Income Statement and Balance Sheet and the advanced DuPont decomposition of ROE. Assume that the tax rate is 35%. ROE = RNOA + FLEV * SPREAD Notes: ● ROE: Return on Equity: Ratio of Net Income to Average Stockholders’ Equity ● RNOA: Return on Net Operating Assets: Ratio of Net Operating Income to Average Net Operating Assets ● NBC: Net Borrowing Costs: Ratio of Net Financial Expenses to Net Financial Obligations (NFO) ● FLEV: Financial Leverage: Ratio of NFO to Average Stockholders’ Equity ● SPREAD: Difference between RNOA and NBC Discussion Question 5: Advanced DuPont Analysis Below are the condensed Income Statement and Balance Sheet of ABC Ltd. Prepare the Reformulated Income Statement and Balance Sheets (for 2022 and 2023). What do you notice about net financial obligations and net financial expenses? How do you think such a capital structure will affect ROE? Discussion Question 6: Ratio Analysis The Table below presents some financial ratios (from DatAnalysis Premium) of Kogan Ltd (ASX:KGN) for the period 2019-2023. Analyse the company’s liquidity and solvency based on this information. Also, using the information provided, comment on whether the company’s capital structure is optimal.
Writing an Empirical Economics Paper This document contains instructions for writing an empirical economics paper. The Structure of the Empirical Paper Empirical papers in economics have a consistent look and feel. Follow the usual outline: Title Page: Includes title, your name, date, and anyone you want to thank for help Abstract: In 100 words or less, state the main contribution or finding. I. Introduction A. Statement of the topic and question to be analyzed B. Rationale for choice of the topic (or why you find this interesting) C. Explanation of the organization of the remainder of the paper II. Literature Review Choose some form (e.g., chronological or thematic) to organize the literature review. Mere listing and summary of several sources is not acceptable. A good literature review interweaves the various articles in a seamless way. III. Theoretical Analysis Present a brief version of a model or highlight the theoretical source of the hypothesis to be tested. IV. Empirical Analysis (the main and longest part of the empirical paper) A. The Data i. Provide sources on all variables ii. Provide summary statistics on all variables in a well-organized table B. Presentation and Interpretation of Results V. Conclusion A. Restate the topic or question that was analyzed B. Provide your answer or conclusion, and compare to previous results in the literature C. Point out the best areas for further research VI. References Key Style Issues . Use the outline labeling scheme and section headings (e.g., IV.A.ii Summary Statistics) to organize your paper. . Citation style.: When referring to someone’s work, simply list the author’s last name and publication year (e.g., Jones [2004]). The full citation is in the references section. . Display regression results in the standard table format (see below for more detail). Literature Review A literature review is a summary of what other people have thought about your question or questions closely related to your topic. More specifically, it should explain how others have dealt with the issues you will be addressing in your paper. The literature review usually serves two equally important purposes. First, it will explain how others have tackled your question. Second, it will provide you with some theory (economic or otherwise) which you can use in trying to answer the question or test someone else's answer. The quality of your review depends on the quality of the papers you include, how on point they are, and your ability in distilling and presenting the findings in the literature. You may certainly read nonprofessional sources like Newsweek or google your research question in order to stimulate the development of a policy topic, but these sources are not suitable for upper- level undergraduate research. Do not rely on mass media sources for your literature review. For your literature review, you need work published in professional, journals. JSTOR, www.jstor.org, is an archive that contains the full text of a select group of journals in economics and other disciplines up through about four years ago (this varies from journal to journal). It is a good place to start, but you will want to go beyond JSTOR. The references of the papers you find can lead you to other interesting papers and make your literature search easier. Once you find a single paper that addresses your research question, its bibliography is a gold mine of other papers that asked that question, or related questions. Citation is important. After paraphrasing findings or explicitly quoting text, give credit by simply listing the last name of the author (use “et al.” when there are more than two authors) and year of publication. Do not include the entire reference in the text of your paper or in a footnote. Here is an example: “Smith [2003] finds that more schooling lowers the probability of smoking.” In the references, a full citation of the Smith [2003] article is presented. A standard referencing format you can use is the Chicago style. http://www.wisc.edu/writing/Handbook/DocChicago.html Be warned of the dangers of plagiarism. It is very easy to plagiarize someone's work unintentionally; but this fact does not make plagiarism any less serious of an offense. Make certain that you either directly quote and attribute the quote, or paraphrase the source (no more than three consecutive words alike). Remember this: In general, direct quotation should be used sparingly in an economics research paper. Repeated use of direct quotation gives the impression of laziness and is often disruptive of your own style and method of organization. A good strategy is to make sure that you paraphrase the work when you are actually taking the notes from the source, in case you forget to do so later on. Remember that the whole point of a literature review is to present others' work—your contribution will come a bit later. It is perfectly acceptable to say something like, "In his recent book on medical malpractice, Smith [2003] contends that ..." Theoretical Section "Why is a theory section needed in an empirical paper?" Because a complete answer to your question must rely on theory and data. You will need some theory to guide you in deciding which variables are relevant for your question. Common sense alone is not a sufficient reason for including or excluding certain variables in your analysis. Theory can also help in choosing the functional form and whether or not autocorrelation or heteroskedasticity are part of the data generation process. In some cases, the theory section is quite clear. For example, earnings function papers have a solid theoretical foundation that underlies the use of the semi-log functional form. If your paper utilizes a measure of earnings as the dependent variable, you can present a theoretical argument for using the semi-log form. as well as, for comparison, a regression that uses wage as the dependent variable. However, it is also possible that there is no well developed theory for your question. In this case, it is common to see the literature review and theoretical sections combined. Your functional form and explanatory variables are chosen based on the work of others. The theoretical section is a difficult piece of the empirical paper because some questions have precious little theory behind them. Even those questions that do have a solid theoretical foundation are often difficult to explain. When deciding what to say in terms of the theory section, remember that you are writing an empirical paper so the main function of the theory is to justify your empirical work. In other words, use the theoretical section to explain why you chose the particular explanatory variables you selected and the functional forms you used. Empirical Results This is the most important part of your paper. It is always divided into two main subsections: the data and the results. The Data Do not forget to provide the sources of your data and to help the reader by making a table that offers summary statistics on each variable. You should define each variable carefully and, if necessary, point out how the empirical measure deviates from its theoretical counterpart. Typical summary statistics that are offered include: max, min, average, and SD values for each variable. It is not unusual to offer histograms and other information for variables with skewed distributions. Excel is a fabulous tool here, and it is easy to get carried away. Remember, your goal should be clarity! This subsection is the place to offer interesting information about the data. You should also point out the limitations, if any, of your data. You will want to describe your procedure in obtaining the data, making sure to point out key decisions in how you drew your sample. For example, in describing the wage variable, you might explain that you decided to remove all observations with negative values. You will want to clearly state the time period (survey month and year, if CPS data) of your data set. Do not go into excruciatingly painful detail on every step of your data collection. Presentation and Interpretation of Results This subsection is the heart of an empirical paper. Having set out the question, reviewed the previous literature, explored the theoretical perspective, and collected data, you are finally ready to do some econometrics. Use subheadings to lead the reader through the different levels of your analysis. You might start with a table that compares averages for two groups, then move to a regression analysis, considering a variety of specifications and different sets of explanatory variables. You may also want to have a subheading for advanced analyses, such as robust standard errors. You do not need to report every regression you run. If you ran multiple models, use a table to report your results. The table is used to easily display the results from various models and invites comparison of coefficients. Below is a template you can use to organize your results: Model 1: Dependent Variable Model 2: Dependent Variable Intercept Est. Coefficient (est. SE) Est. Coefficient (est. SE) X1 Est. Coefficient (est. SE) Est. Coefficient (est. SE) X2 Est. Coefficient (est. SE) X3 Est. Coefficient (est. SE) X4 Est. Coefficient (est. SE) X42 n R2 The table shows how the first regression has no control variables. It is a simple, bivariate regression of X1 on the dependent variable. Model 2 adds three explanatory variables (presumably selected on the basis of some theoretical reasoning). Notice how the table invites comparison of the models. In the discussion of the results, you would explain the results from each model and offer your opinion on the best answer to your research question. The table can be augmented with asterisks (for statistically significant coefficient estimates) or other information (e.g., DW statistics for autocorrelation). You can add notes at the bottom as needed. To be sure, there is no consensus on the matter of significant figures in the economics profession. One thing that is quite clear is that reporting ten or fifteen decimal places is silly and embarrassing. Avoid this. Some rounding must be applied to computer output. While applying “pleasing to the eye,” the common practice in the social sciences, is better than nothing, you can do better by considering the likely size of the error in the results. Writing up your results Here is a list of good practices that should help you in writing up your results: ● Motivate the error term: Begin the results subsection with a paragraph or two that explains the functional form. you are using and why there is a random disturbance term. What is the source of chance error in your data generation process? ● Produce a table to present the results of various regressions. Use this table to discuss and compare the various models. ● Interpret your results: Explicitly mention the estimated coefficient of the crucial explanatory variable in your analysis and comment on what it means. ● Provide units: When discussing numbers, such as estimated coefficients or predicted Y values, remember to present the units of the numbers. ● If you are testing a hypothesis, present the null hypothesis, compute the test statistic, and report the P-value. State whether you reject or do not reject the null. ● If you are estimating a parameter, report the estimated SE and a 95% confidence interval. ● Discuss whether or not a coefficient is practically important—i.e., comment on the magnitude of the coefficient. ● If needed, compute and interpret elasticities. ● Compare your results to others in the literature. Do they support or contradict the relevant economic theory? At the end of the empirical section of your paper, you should be able to draw a conclusion, even if it is a negative one. For example, you may find that there is no relationship between divorce and schooling in your data; this is still worth reporting. Remember this: No study is absolutely perfect, but if you have done a thorough job in your empirical section, you should be able to reach some answer to your research question. This conclusion will then be inserted into your introductory paragraph in a slightly different form. Things to Avoid Here are common mistakes and poor practices to avoid like the plague: ● Writing out a long equation with a beta in front of each variable. This is silly because the regression results table will list the variables in each model. ● Even worse is: y = β0 + β1x1 + β2 x2 + … + βkxk + ε . This has zero information content. ● Splitting tables over more than one page. Make every effort (adjusting font size and column width) to keep an entire table on the same page. ● Repeating the same information, e.g., n = 12’662, for each variable in a summary statistics table. This is visible noise pollution. Simply put n = 12’662 at the bottom of the table. ● Referring to a paper by an author’s first name or title such as Mr. or Dr. Use last name [year]. Conclusion In the conclusion, your job is to give the paper's greatest hits. That is, you should restate your research question, give the high points of the literature survey and theory, remind your reader of the data and the methods you used, and restate your conclusion. You may then go on to talk about the limitations of your analysis, any data you wish you could have garnered but couldn't, and what you would have liked to have done with your analysis but couldn't given the time limitations. This needn't be a long section—do not apologize for your work, but do suggest avenues for further research. After writing the conclusion, you should then go to the beginning of the paper and write the Introduction. It should be a snap. "And then I turn it in?" No, not quite yet. The last thing you should do is PROOFREAD your paper. Even after spell checking the paper with your word processor, you should take the time to read it one last time before turning it in. Fix typographical errors, improve wording, and make sure the numbers make sense. Your paper will be evaluated with the rubric below. The rubric relies on the material presented above. Follow these instructions and you will write a solid paper.
Economics 201 Microeconomics Tutorial 8 Question 1: Consider a natural monopoly with declining average cost curve summarized by the equation C = 16 +Q where C is in dollars and Q is in millions of units. Demand for the natural monopolist’s service is given by P = 11 – Q. (i) Suppose this monopolist operates as an unregulated monopolist and is allowed to charge the monopoly price. Determine the price and output of the unregulated monopolist. (ii) On the other hand suppose that the monopolist is regulated by the State and the State Regulatory Board institutes average cost pricing. What is the appropriate price and quantity? Question 2: A golf course operator must decide what “greens fees” (prices) to charge on rounds of golf. Daily demand during the week is Pd = 36 – Qd/10 where Qd is the number of 18-hole rounds and Pd is the price per round. Daily demand on the weekend is Pw = 50 – Qw/12. Assume that wear and tear on the golf course is negligible, i.e. the marginal cost is zero. The operator only has fixed costs. This implies that in this situation maximizing profit is analogous to maximizing revenue. So for the rest of this problem just compare revenues. (i) What prices should the operator charge for each round during (1) the week and (2) the weekend? (ii) Suppose the operator did not charge separate prices during the week and the weekend. He treats weekend and weekday demand combined as one market and sets the same price for both. What price would he charge in that case? (ii) Show that the revenue he gets in Part (i) exceeds that in Part (ii). Question 3: A cruise line has space for 500 passengers on each voyage. There are two market segments: elderly passengers and younger passengers. The demand curve for the elderly market segment is Q1 = 750 – 4P1. The demand curve for the younger market segment is Q2 = 850 – 2P2. In each equation, Q denotes the number of passengers on a cruise of given length and P denotes the price per day. The marginal cost of serving a passenger of either type is $40 per person per day. (i) Assuming the cruise line can price discriminate, what is the profit-maximising number of passengers of each type? (ii) What is the profit maximising price for each type of customer?
The Language of Propositional Logic Introduction Consider the following argument: Whenever it rains, the grass gets wet. The grass is dry. Hence, it is not raining. If we let • R denote “It is raining,” • W denote “The grass is wet,” • ¬ denote “it is not the case that,” and • → denote “implies that,” then the above argument can be formalized as (R → W) ¬W ¬R The Language of Propositional Logic In order to discuss simple arguments like the one we have just seen, we need to set up a suitable framework. For this, we use the language of propositional logic. Just as the English language is made up of words that are formed from letters, the language of propositional logic will be made up of formulas that are formed from symbols. Definition The following are the symbols of propositional logic, arranged into three groups. • Propositional variables: P1, P2, P3, P4, P5, . . . • Connectives: ¬, → • Brackets: (, ) Notation: We will often use the letters P, Q, R, S to denote propositional variables. Propositional Formulas In English, words are finite strings from the alphabet, but not all finite strings of letters are words. In propositional logic, certain finite strings from the symbol set will be called formulas. Later, when we assign meaning to our language, the formulas of propositional logic will correspond to statements which can be either true or false. Definition Propositional formulas are certain finite strings of symbols, defined inductively as follows: (1) All propositional variables are formulas. (2) If ϕ is a formula, so is ¬ϕ. (3) If ϕ and ψ are formulas, so is (ϕ → ψ). So the formulas are built up from propositional variables using the connectives. Question Which of the following are formulas? For those that are, show how they are built up from the propositional variables. 1. ¬¬¬P 2. P → Q → R 3. ()P 4. ¬(¬P → R) 5. (¬P) Induction and Subformulas Propositional Formulas Since formulas are built up inductively from propositional variables using the connectives ¬ and →, we can use the method of mathematical induction to prove facts about formulas. The base case will be to prove the fact about propositional variables. There will be two inductive steps, one for each of • formulas of the form. ¬ϕ, assuming we know the fact holds for ϕ, and • formulas of the form. (ϕ → ψ), assuming the fact holds for ϕ and ψ. Question Which of the following are subformulas of (¬(P → Q) → (Q → P))? 1. ¬P 2. ¬Q 3. (Q → P) 4. → P 5. (¬(P → Q) → (Q → P)) Truth Assignments and Truth Tables Truth Assignments We are now ready to give meaning to our propositional formulas. Definition A truth assignment is a function that assigns a truth value of T (true) or F (false) to every propositional variable. That is, a truth assignment is a function e : {P1, P2, P3, . . .} → {T, F} If e is a truth assignment, then we extend e to be a function eˆ on all formulas as follows: • If ϕ = P, a propositional variable, then eˆ(ϕ) = e(ϕ). • If ϕ = ¬ψ where we have defined eˆ(ψ), then eˆ(ϕ) = T if eˆ(ψ) = F, otherwise eˆ(ϕ) = F. • If ϕ = (ψ → χ) where we have defined eˆ(ψ) and eˆ(χ), then eˆ(ϕ) = F if eˆ(ψ) = T and eˆ(χ) = F, and eˆ(ϕ) = T otherwise. Normally, we simply write e in place of eˆ. Questions 1. Let e be a truth assignment such that e(P) = T, e(Q) = T, and e(R) = F. Find e((P → (R → ¬Q))). 2. Let e be the truth assignment given by Find e(((¬P4 → P3) → (P18 → ¬P1))).
