In Exercises 1–4, calculate the expected payoff of the game with payoff matrix
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Chapter 4 Solutions
Finite Mathematics
- 3. A large retail company posted sales/revenues of $29.08 billion in 2015. The company's sales growth was dpproxmately 0.4)0DELWeen 2013 and 2016. Assuming the sales/revenue growth continues at the same rate, what are the expected sales/revenues in 2020? $36.24 billion $40.19 billion $37.79 billion O $39.66 billionarrow_forwardexercise #32arrow_forwardDiscuss two extensions to the original GARCH (p,q) model and explain additional characteristics of financial data they might be able to capture.arrow_forward
- Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493. Old Faithful Using the listed duration and interval after times, find the best predicted “interval after” time for an eruption with a duration of 253 seconds. How does it compare to an actual eruption with a duration of 253 seconds and an interval after time of 83 minutes?arrow_forwardAn investor is concerned with the market return for the coming year, where the market return is defined as the percentage gain (or loss, if negative) over the year. The investor believes there are five possible scenarios for the national economy in the coming year: rapid expansion, moderate expansion, no growth, moderate contraction, and serious contraction. Furthermore, she has used all of the information available to her to estimate that the market returns for these scenarios are, respectively, 23%, 18%, 15%, 9%, and 3%. That is, the possible returns vary from a high of 23% to a low of 3%. Also, she has assessed that the probabilities of these outcomes are 0.12, 0.40, 0.25, 0.15, and 0.08. Use this information to describe the probability distribution of the market return. Compute the following for the probability distribution of the market return for the coming year.: 1. Mean, 2. Variance, 3. Standard deviation Show your solutions.arrow_forwardAnalyze the payoff Matrix belowarrow_forward
- Hermann Ebbinghaus (1850–1909) pioneered the study of memory. A 2011 article in the Journal of Mathematical Psychology presents the mathematical model R(t) = a + b(1 + ct)−? for the Ebbinghaus forgetting curve, where R(t) is the fraction of memory retained t days after learning a task; a, b, and c are experimentally determined constants between 0 and 1; ? is a positive constant; and R(0) = 1. The constants depend on the type of task being learned. (a) What is the rate of change of retention t days after a task is learned?arrow_forwardSolve the equations in Exercises 1–16 by the method of undeterminedcoefficients.arrow_forwardThere is some evidence that, in the years 1981— 85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6 pp. 320— 35, 1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.76%, with a standard deviation of 0.12%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years. (a)According to Chebyshev's theorem,…arrow_forward
- International Visitors The number of internationalvisitors to the United States for selected years 1986–2010 is given in the table below. If you had to pick one of these models to predictthe number of international visitors in the year2020, which model would be the more reasonablechoice?arrow_forward10 There is some evidence that, in the years 1981 – 85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6, pp. 320 - 35, 1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.79%, with a standard deviation of 0.16%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years. (a) According to Chebyshev's theorem, at…arrow_forwardQuestion 1 Consider the CCAPM model and the following equation for the price of an asset in equilibrium: 1 C: (mi+1, Tt+1) + -E: (x+1), 1+Rf Pt = is the price of the asset at time t; x++1 is the payoff of the asset at time t+1; Rf indicates the return on the risk-free asset; m+1 is the stochastic discount factor; and E, and C; denote the conditional expectation and the conditional covariance given time-t information, respectively. where Pt Which of the following is true? A) The asset sells at a premium and the covariance term in the equation above is positive B) The asset sells at a premium and the covariance term in the equation above is positive if the asset gives a high payoff when consumption is low C) The asset sells at a premium and the covariance term in the equation above is positive if th asset gives a high payoff when consumption is high D) The asset sells at a premium and the covariance term in the equation above is negative if the asset gives a high payoff when consumption…arrow_forward
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