EBK USING & UNDERSTANDING MATHEMATICS
7th Edition
ISBN: 8220106844434
Author: Briggs
Publisher: PEARSON
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Chapter 3.C, Problem 38E
Source of Error. Describe possible source of random and systematic errors in the following measurements.
42. The number of votes cast for two candidates in a U.S. Senate race
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To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow:
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2
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School B
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157
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145
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Suppose a sign test for matched pairs with a 1% level of significance is used to test the hypothesis that the schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools have different levels of effectiveness in teaching reading skills. Let p denote portion of positive signs when the scores of school B are subtracted from the corresponding scores of school…
Chapter 3 Solutions
EBK USING & UNDERSTANDING MATHEMATICS
Ch. 3.A - The price of a meal at a four-star restaurant is...Ch. 3.A - The population of a town increases from 50,000 to...Ch. 3.A - Suppose the value of a home changed by -20% over...Ch. 3.A - Emily scored 50% higher on the SAT than Joshua....Ch. 3.A - The price of a movie ticket increased from $10 to...Ch. 3.A - Your receipt shows that you paid $47.96 for a new...Ch. 3.A - Consider this statement: “The interest rate on...Ch. 3.A - A friend has a textbook that originally cost $150....Ch. 3.A - You currently earn $1000 per month, but you are...Ch. 3.A - During high school, Elise won 30% of the swim...
Ch. 3.A - Describe the three basic uses of percentages. Give...Ch. 3.A - Distinguish between absolute and relative change....Ch. 3.A - Distinguish between absolute and relative...Ch. 3.A - Explain the difference between the key words of...Ch. 3.A - Explain the difference between the terms percent...Ch. 3.A - 6. Give an example to explain why, in general, it...Ch. 3.A - In many European countries, the percentage change...Ch. 3.A - The price of tuition has tripled since my parents...Ch. 3.A - I’ve decreased my caloric intake by 125% which has...Ch. 3.A - If you earn 20% more than I do, then I must earn...Ch. 3.A - If they raise taxes by 10% every year, in a decade...Ch. 3.A - We found that these rare cancers were 700% more...Ch. 3.A - The rate of return on our fund increased by 50%,...Ch. 3.A - My bank increased the interest rate on my savings...Ch. 3.A - Prob. 15ECh. 3.A - Prob. 16ECh. 3.A - Prob. 17ECh. 3.A - Prob. 18ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 20ECh. 3.A - Prob. 21ECh. 3.A - Prob. 22ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 25ECh. 3.A - Prob. 26ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 28ECh. 3.A - Prob. 29ECh. 3.A - Prob. 30ECh. 3.A - Prob. 31ECh. 3.A - Prob. 32ECh. 3.A - Prob. 33ECh. 3.A - Compare the following pairs of numbers A and B in...Ch. 3.A - 31-36: Review of Ratios. Compare the following...Ch. 3.A - Review of Ratios. Compare the following pairs of...Ch. 3.A - Prob. 37ECh. 3.A - Prob. 38ECh. 3.A - Prob. 39ECh. 3.A - Percentages as Fractions in the following...Ch. 3.A - Prob. 41ECh. 3.A - Prob. 42ECh. 3.A - Salary Comparisons. Clint’s salary increased from...Ch. 3.A - 44. Population Comparison. Between the 2010 U.S....Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Prob. 51ECh. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - 57-60: Prices and Sales. Fill in the blanks in the...Ch. 3.A - Prob. 58ECh. 3.A - Prob. 59ECh. 3.A - Prob. 60ECh. 3.A - Percentages of Percentages. Describe each of the...Ch. 3.A - 61-64: Percentages of Percentages. Describe each...Ch. 3.A - Percentages of Percentages. Describe each of the...Ch. 3.A - Percentages of Percentages. Describe each of the...Ch. 3.A - Care in Wording. Assume that 30% of city employees...Ch. 3.A - Ambiguous News. The average annual precipitation...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Shifting Reference Value. State whether the...Ch. 3.A - Prob. 72ECh. 3.A - Prob. 73ECh. 3.A - Shifting Reference Value. State whether the...Ch. 3.A - Prob. 75ECh. 3.A - Is It Possible? Determine whether the following...Ch. 3.A - Prob. 77ECh. 3.A - Prob. 78ECh. 3.A - 75-80: Is It Possible? Determine whether the...Ch. 3.A - 75-80: Is It Possible? Determine whether the...Ch. 3.A - 81. Average Percentages. Suppose you have an 80%...Ch. 3.A - Prob. 82ECh. 3.A - 83-86: Analyzing Percentage Statements. Assuming...Ch. 3.A - Prob. 84ECh. 3.A - 83-86: Analyzing Percentage Statements. Assuming...Ch. 3.A - Prob. 86ECh. 3.A - 87-90: Solving Percentage Problems. Solve the...Ch. 3.A - Prob. 88ECh. 3.A - Prob. 89ECh. 3.A - 87-90: Solving Percentage Problems. Solve the...Ch. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Prob. 94ECh. 3.A - 108. Stock Market Losses.
a. The largest...Ch. 3.A - Percentages. Find three recent news reports that...Ch. 3.A - Percentage Change. Find a recent news report that...Ch. 3.A - Prob. 98ECh. 3.B - 1. The number 300,000,000 is the same as a. 3 10 7...Ch. 3.B - Prob. 2QQCh. 3.B - Prob. 3QQCh. 3.B - 4. You are asked to estimate the total amount of...Ch. 3.B - 5. You are wondering how many dollar bills you’d...Ch. 3.B - 6. You are given some data and asked to calculate...Ch. 3.B - You are looking at a map with a scale of 1 inch =...Ch. 3.B - An NFL quarterback is offered a new contract...Ch. 3.B - You are running for mayor this year in a city with...Ch. 3.B - A lottery ticket on which the odds of winning are...Ch. 3.B - Briefly describe scientific notation. How is it...Ch. 3.B - Prob. 2ECh. 3.B - Prob. 3ECh. 3.B - Explain how we can use comparisons to put numbers...Ch. 3.B - 5. Describe three common ways of expressing the...Ch. 3.B - 6. Explain how we can use scaling to put numbers...Ch. 3.B - 7. Suppose that the Sun were the size of a...Ch. 3.B - 8. Describe several ways of putting each of the...Ch. 3.B - Prob. 9ECh. 3.B - I’ve seen about commercials on TV.Ch. 3.B - I work in an office building that is 300 feet...Ch. 3.B - In total, Americans spend about a billion dollars...Ch. 3.B - A popular local redtaurant serves 5 million...Ch. 3.B - The CEO of the company earned more money last year...Ch. 3.B - Prob. 15ECh. 3.B - Prob. 16ECh. 3.B - Review of Scientific Notation. In the following...Ch. 3.B - Review of Scientific Notation. In the following...Ch. 3.B - Prob. 19ECh. 3.B - Prob. 20ECh. 3.B - Prob. 21ECh. 3.B - Prob. 22ECh. 3.B - Prob. 23ECh. 3.B - Prob. 24ECh. 3.B - Prob. 25ECh. 3.B - 23-26: Using Scientific Notation. Rewrite the...Ch. 3.B - Prob. 27ECh. 3.B - Prob. 28ECh. 3.B - 29-32: Perspective Through Estimation. Use...Ch. 3.B - Perspective Through Estimation. Use estimation to...Ch. 3.B - Perspective Through Estimation. Use estimation to...Ch. 3.B - Prob. 32ECh. 3.B - Prob. 33ECh. 3.B - Prob. 34ECh. 3.B - Prob. 35ECh. 3.B - Order of Magnitude Estimates. Make order of...Ch. 3.B - Prob. 37ECh. 3.B - Prob. 38ECh. 3.B - Prob. 39ECh. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - Prob. 43ECh. 3.B - Prob. 44ECh. 3.B - Prob. 45ECh. 3.B - Prob. 46ECh. 3.B - Prob. 47ECh. 3.B - Prob. 48ECh. 3.B - Scale Ratios. Find the scale ratios for the...Ch. 3.B - Prob. 50ECh. 3.B - Scale Model Solar System. The following table...Ch. 3.B - 54. Interstellar Travel. The fastest spaceships...Ch. 3.B - 53. Universal Timeline. According to modern...Ch. 3.B - Universal Clock. According to modern science,...Ch. 3.B - Prob. 55ECh. 3.B - Prob. 56ECh. 3.B - Prob. 57ECh. 3.B - Prob. 58ECh. 3.B - Prob. 59ECh. 3.B - Prob. 60ECh. 3.B - Making Numbers Understandable. Restate the...Ch. 3.B - Making Numbers Understandable. Restate the...Ch. 3.B - Cells in the Human Body. Estimates of the number...Ch. 3.B - Emissions. For every gallon of gasoline burned by...Ch. 3.B - Prob. 65ECh. 3.B - Wood for Energy? A total of about 180,000...Ch. 3.B - Stellar Corpses: White Dwarfs and Neutron Stars. A...Ch. 3.B - Until the Sun Dies. It took 65 million years from...Ch. 3.B - Personal Consumption. The Bureau of Economic...Ch. 3.B - Sampling Problems. Sampling techniques can be used...Ch. 3.B - Prob. 71ECh. 3.B - 72 – 75 : Sampling Problems. Sampling techniques...Ch. 3.B - Sampling Problems. Sampling techniques can be used...Ch. 3.B - 76. Energy Comparisons. Using data available from...Ch. 3.B - Prob. 75ECh. 3.B - Prob. 76ECh. 3.B - Prob. 77ECh. 3.B - Prob. 78ECh. 3.B - Prob. 79ECh. 3.B - Putting Numbers in Perspective. Find at least two...Ch. 3.B - Prob. 81ECh. 3.C - The $5.6 trillion surplus that government...Ch. 3.C - Under the standard rules for counting significant...Ch. 3.C - Under the standard rules for counting significant...Ch. 3.C - You are trying to measure the outside temperature...Ch. 3.C - You are trying to measure the outside temperature...Ch. 3.C - A testing service makes a error that causes all...Ch. 3.C - A testing service makes an error that causes all...Ch. 3.C - A digital scale shows that you weigh 112.7 pounds,...Ch. 3.C - At a particular moment, the U.S. National Debt...Ch. 3.C - Prob. 10QQCh. 3.C - Prob. 1ECh. 3.C - Prob. 2ECh. 3.C - Prob. 3ECh. 3.C - Distinguish between accuracy and precision. Give...Ch. 3.C - Why can it be misleading to give measurements with...Ch. 3.C - Prob. 6ECh. 3.C - Next year's federal deficit will be $443.45...Ch. 3.C - In many developing nations, official estimates of...Ch. 3.C - My height is 5 feet, 6.3980 inches.Ch. 3.C - Wilma used her paces to measure the dimensions of...Ch. 3.C - More precision is useless if the measurement is...Ch. 3.C - A $2 million error is a lot of money, but it...Ch. 3.C - Prob. 13ECh. 3.C - 13-14: Review of Rounding. In the following...Ch. 3.C - 15-26: Counting Significant Digits. State the...Ch. 3.C - Prob. 16ECh. 3.C - Prob. 17ECh. 3.C - Prob. 18ECh. 3.C - Prob. 19ECh. 3.C - Prob. 20ECh. 3.C - Prob. 21ECh. 3.C - Prob. 22ECh. 3.C - Counting Significant Digits. State the number of...Ch. 3.C - 15-26: Counting Significant Digits. State the...Ch. 3.C - 15-26: Counting Significant Digits. State the...Ch. 3.C - 17-28: Counting Significant Digits. State the...Ch. 3.C - Prob. 27ECh. 3.C - Prob. 28ECh. 3.C - Prob. 29ECh. 3.C - Prob. 30ECh. 3.C - Prob. 31ECh. 3.C - Prob. 32ECh. 3.C - Prob. 33ECh. 3.C - Prob. 34ECh. 3.C - Source of Error. Describe possible source of...Ch. 3.C - 33-38: Sources of Error. Describe possible sources...Ch. 3.C - 35-42: Source of Error. Describe possible source...Ch. 3.C - Source of Error. Describe possible source of...Ch. 3.C - Tax Audit. A tax auditor reviewing a tax return...Ch. 3.C - Prob. 40ECh. 3.C - Safe Air Travel. Before taking off, a pilot is...Ch. 3.C - Cutting Lumber. A lumber yard employee cuts 30...Ch. 3.C - Prob. 43ECh. 3.C - Prob. 44ECh. 3.C - Prob. 45ECh. 3.C - Prob. 46ECh. 3.C - 43-50: Absolute and Relative Errors. Find the...Ch. 3.C - 43-50: Absolute and Relative Errors. Find the...Ch. 3.C - 43-50: Absolute and Relative Errors. Find the...Ch. 3.C - Prob. 50ECh. 3.C - Prob. 51ECh. 3.C - Accuracy and Precision. For each pair of...Ch. 3.C - Prob. 53ECh. 3.C - Accuracy and Precision. For each pair of...Ch. 3.C - Prob. 55ECh. 3.C - Prob. 56ECh. 3.C - Prob. 57ECh. 3.C - Prob. 58ECh. 3.C - 55-62: Combining Numbers. Use the appropriate...Ch. 3.C - 59-66: Combining Numbers. Use the appropriate...Ch. 3.C - 55-62: Combining Numbers. Use the appropriate...Ch. 3.C - Prob. 62ECh. 3.C - Prob. 63ECh. 3.C - Prob. 64ECh. 3.C - Prob. 65ECh. 3.C - Prob. 66ECh. 3.C - Prob. 67ECh. 3.C - Prob. 68ECh. 3.C - Prob. 69ECh. 3.C - Prob. 70ECh. 3.C - 75. Propagation of Error. Suppose you want to cut...Ch. 3.C - 72. Analyzing a Calculation. According to 2015...Ch. 3.C - 77. Random and Systematic Errors. Find a recent...Ch. 3.C - Prob. 74ECh. 3.C - Prob. 75ECh. 3.C - Prob. 76ECh. 3.C - Prob. 77ECh. 3.D - Look at the gasoline price index in Table 3.2....Ch. 3.D - Prob. 2QQCh. 3.D - Prob. 3QQCh. 3.D - Prob. 4QQCh. 3.D - Prob. 5QQCh. 3.D - 6. Suppose we created a price index for computers,...Ch. 3.D - 7. Over the past three decades, the cost of...Ch. 3.D - Suppose your salary has been rising at a greater...Ch. 3.D - Prob. 9QQCh. 3.D - Prob. 10QQCh. 3.D - Prob. 1ECh. 3.D - What is the Consumer Price Index (CPI)? How is it...Ch. 3.D - Prob. 3ECh. 3.D - Prob. 4ECh. 3.D - Prob. 5ECh. 3.D - Even though my salary has remained the same for...Ch. 3.D - Benjamin Franklin said, “A penny saved is a penny...Ch. 3.D - The prices of cars have risen steadily, but when...Ch. 3.D - 9. When we chart today’s price of milk in 1995...Ch. 3.D - 10. The Consumer Price Index is a theoretical...Ch. 3.D - 11-16: Gasoline Price Index. Use Table 3.2 to...Ch. 3.D - Prob. 12ECh. 3.D - Prob. 13ECh. 3.D - Prob. 14ECh. 3.D - Prob. 15ECh. 3.D - Prob. 16ECh. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - HealthCare Spending. Total spending on health care...Ch. 3.D - Airfare. According to the U.S. Bureau of...Ch. 3.D - Private College Cost. According to the College...Ch. 3.D - Public College Cost. According to the College...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Prob. 39ECh. 3.D - Prob. 40ECh. 3.D - Prob. 41ECh. 3.D - Prob. 42ECh. 3.D - Fan Cost Index. The cost of attending a Major...Ch. 3.D - Price of Gold. The price of gold (end-of-year...Ch. 3.D - 45. Economic Freedom Index. The Heritage...Ch. 3.D - Consumer Price Index. Find a recent news report...Ch. 3.D - Prob. 47ECh. 3.D - Prob. 48ECh. 3.D - Consumer Confidence Index. Use a search engine to...Ch. 3.D - Prob. 50ECh. 3.D - Prob. 51ECh. 3.D - Prob. 52ECh. 3.D - Inflation Calculator. Use the Bureau of Labor...Ch. 3.D - Prob. 54ECh. 3.D - 51-56: Inflation Calculator. Use the Bureau of...Ch. 3.D - 51-56: Inflation Calculator. Use the Bureau of...Ch. 3.E - Study Table 3.5. What does the number “8” in the...Ch. 3.E - Study Table 3.5. Which statement is not supported...Ch. 3.E - During their freshman year, Derek’s GPA was 3.4...Ch. 3.E - A false negative in a cancer screening test means...Ch. 3.E - A false positive in a test for steroids means that...Ch. 3.E - Study Table 3.7. The total number of women who did...Ch. 3.E - Study Table 3.7. The total number of women whose...Ch. 3.E - Suppose that a home pregnancy test is 99%...Ch. 3.E - Study the graph in Figure 3.5a. Which of the...Ch. 3.E - Study the graph in Figure 3.5b. Which of the...Ch. 3.E - Prob. 1ECh. 3.E - Briefly explain why a positive result on a...Ch. 3.E - Prob. 3ECh. 3.E - Prob. 4ECh. 3.E - Despite the fact that the new drug lowered blood...Ch. 3.E - Our total class score is based only on homework...Ch. 3.E - Baggage screening machines are 98% accurate in...Ch. 3.E - The polygraph test showed that the suspect was...Ch. 3.E - The Republications claim the tax cut benefits...Ch. 3.E - The agency suffered a real cut in its annual...Ch. 3.E - Batting Percentages. The table below shows the...Ch. 3.E - 12. Jeter and Justice. The following table shows...Ch. 3.E - Test Scores. The table below shows eighth-grade...Ch. 3.E - Test Scores. Consider the following table...Ch. 3.E - Prob. 15ECh. 3.E - Prob. 16ECh. 3.E - Prob. 17ECh. 3.E - Disease Test. Suppose a test for a disease is 90%...Ch. 3.E - Performance Enhancement. Suppose that a test for...Ch. 3.E - Prob. 20ECh. 3.E - Political Math. Government spending for a popular...Ch. 3.E - 29. A Tax Cut. According to an analysis of a...Ch. 3.E - Basketball Records. Consider the following...Ch. 3.E - 22. Better Drug. Two drugs, A and B, were tested...Ch. 3.E - Prob. 25ECh. 3.E - Prob. 26ECh. 3.E - Airline Arrivals. The following table shows real...Ch. 3.E - Prob. 28ECh. 3.E - Drug Testing. Explore the issue of drug testing...Ch. 3.E - Prob. 30ECh. 3.E - Prob. 31E
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- Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 34.4 27.1 30.8 28.0 32.2 27.6 32.8 25.2 31.4 33.5 24.7 28.4 Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. Test the sequence for randomness about the median with a 5% level of significance. Verify that the number of runs is 10. What is the upper critical value c2?arrow_forward29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forwardSand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 27.3 34.6 30.6 27.8 33.4 31.5 27.3 31.2 32.0 24.7 24.4 28.2 Test this sequence for randomness about the median. Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives BAABAABAABBB. Verify that the number of runs is 7, the lower critical number is 3, and the upper critical number is 11. Use a 5% level of significance. State the conclusion of the test and interpret your results.arrow_forward
- 29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forward4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.arrow_forward3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.arrow_forward
- 2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…arrow_forwardPlease solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forward
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