Assume that Jay discovers, to his dismay, that his 2014 healthy-state income will be lower than his 2013 healthy-state income, but that his sick-state income IS unchanged from 2013 to 2014. Assume that his healthy-state income in 2013 is IH and his healthy-state income in 2014 is IH −. Assume 0

Assume that Jay discovers, to his dismay, that his 2014 healthy-state income will be lower than his 2013 healthy-state income, but that his sick-state income IS unchanged from 2013 to 2014. Assume that his healthy-state income in 2013 is IH and his healthy-state income in 2014 is IH −. Assume 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What percent of the radios will function for more than 16 years? (b) Suppose the company decides to replace 1% of the radios. Find the length of guarantee period.i.e. find X. (c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years? (d) If 10% of the radios will function for more than X years, find X.
According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0≤t<∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes. 1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering that it is defined for all t≥ 0.) 2. Set up integrals (you can write p(t) for the integrand) for the following probabilities: (a) Waiting longer than 60 minutes. (b) Waiting shorter than 30 minutes. (c) Waiting between 20 and 40 minutes. 3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above) and convert to a percentage with two decimal places.
There is some evidence that, in the years−198185, 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.−32035,1987.) 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 0.86 %, with a standard deviation of 0.10%. 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. According to Chebyshev's theorem, at least 84%…
Vanessa has a utility function for income given by U(I) = VI %3D (that is the square root of income). Because of the nature of her utility function, we know that Vanessa is risk averse. Vanessa is considering an investment that would give her an income of $10,000 with a probability of 0.5 or an income of $15,000 with a probability of 0.5. The expected utility of this investment is (rounded to 2 decimal places): O A. 111.24 O B. 113.48. O C. 118.35. O D. 125.00.
Let i, denote the effective annual return achieved on an equity fund achieved between time (t-1) and time t. Annual log-returns on the fund, denoted by In(1+i), are assumed to form a series of independent and identically distributed Normal random variables with parameters u = 6% and σ = 14%. An investor has a liability of £10,000 payable at time 15. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%.
The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-
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