Question: 2. Let X be an age-at-death random variable with mortality rate (x)=2kx for x0, and where k>0. The mean of the distribution for X is

2. Let X be an age-at-death random variable with mortality rate (x)=2kx for x0, and where k>0. The mean of the distribution for X is 55 . (a) Find Var(X). (b) Find the 90th percentile for the distribution of T(30). (c) Find the 90th percentile for the distribution of T(40). (d) Give an intuitive explanation for why your answer in (c) is less than your answer in (b). (e) Give the mortality rate function for T (40)

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