3.12 An investment firm offers its customers municipal bonds that mature aftervaryinof years. Given that the cumulative distribution function of T,the number of years to maturity for a randomly selected bond, isEmbedded LTIfinda. P(T = 5);b. P(T > 3);c. P(1.4

Here, we are given the cumulative distribution function (CDF) of a random variable T, which…

Answered: 3.12 An investment firm offers its…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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An actuary models loss amounts under a insurance policy using the Pareto distribu- tion. The cdf of the Pareto distribution Suppose that 0 = 1400 and a = 1.6. What is the expected is F(x) = 1 (0/(x+0))ª. payment under a claim given that the policy has a deductible of 350 and a limit of 1300?
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.
Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2,..., Xn fxp(x | p) = (1 – p)*-'p for 0 < p < 1 defined on x E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, B) prior, derive the posterior density of p, fp|X, (p | Xn).
2. Determine whether each of the following distributions are exponential family. For those that are, find a set of complete, minimum sufficient statistics. For those that are not, find a sufficient statistic. (a) Location Exponential: f(x) = e-(-0), x > 0. (b) f(x) = 0(1+x)(1+0), x > 0 (c) logN(u,02): f(x) = 1 a exp{-(log x-μ)²), x > 0. αν2πσ2 },
A researcher is interested in finding out how the past average daily values of the stock prices of a firm A determine the current average daily value of its stock price. Let pt ( measured in dollars) denote the average daily value of the stock price of firm A at time t. The researcher collects data on the average daily values of the stock prices of the last quarter of 2017, i.e., t = 1,2, dots,90 and estimates the following autoregressive model with 1 lag of pt: hat(p)t = 2.48 +.05pt.1bar (R)² = 0.512, SER = 13.14. (1.13) (0.64) The standard errors are given in parentheses. Suppose that the actual average daily value of the stock price on January 2, 2018 was $506.12 and the average daily value of the stock price on December 31, 2017 was $445.12. The forecast error in the estimation of the average daily value of the stock price on January 2, 2018 will be $ (Round your answer to two decimal places.) This is all the info in the question
2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).

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3.12 An investment firm offers its customers municipal bonds that mature after varyin of years. Given that the cumulative distribution function of T, the number of years to maturity for a randomly selected bond, is Embedded LTI find a. P(T = 5); b. P(T > 3); c. P(1.4