Homework Assignment 16: (1) You are the agent for a baseball player who desires an incentive contract that will pay the following amounts: Type of hit Probability of hit per time at bat Compensation per hit Single 0.14 x Double 0.05 2 x Triple 0.02 3 x Home Run 0.03 4 x The number of times at bat has a Poisson distribution with λ = 200. The parameter, x , is determined so that the probability of the player earning at least 4,000,000 is 0.95. Using a normal approximation, determine the player’s expected compensation. (Ans 5,532,122) (2) The random variable, S, has a compound Poisson distribution with λ = 27/16 and claim amounts that are uniformly distributed over [0,32]. The distribution is approximated by a translated gamma distribution. Show that the approximation for Pr(S>10) is given by (3) A surplus process is given by U(t) = u + ct – S(t), t ≥ 0. For times t ≤ 5, the history of claims is given by the table below: Claim Number 1 2 3 4 5 Time of Payment 0.5 1.25 2.75 3.50
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