Question: 6. Suppose that X1, X2, .... are i.i.d. exponential(X) random variables, and that N, independent of the X's has a geometric(p) distribution, i.e., P(N =

6. Suppose that X1, X2, .... are i.i.d. exponential(X) random variables, and that N, independent of the X's has a geometric(p) distribution, i.e., P(N = n) = p(1 - p)"-1, n =1,2, .... Define Y = CALXi. (a) Evaluate E(Y) and var(Y). (by conditioning on N) (b) Compute the Laplace transform or the moment generating function of Y. (again, perhaps, by conditionng on N). (c) Using (b) or otherwise, determine the density fy(y) of the random variable Y

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