Suppose that the time to death X has an exponential distribution with hazard rate A and that the right-censoring time C is exponential with hazard rate 0. Let T Assume that X and C are independent. min(X, C) and 8 = 1 if X < C;0,if X > C. (a) Find P(8 = 1) (b) Find the distribution of T. (c) Show that 8 and T are independent. (d) Let (Ti, 8,),..., (Tn, 8n) be a random sample from this model. Show that the maximum likelihood estimator of d is E, 8;/E- T. Use i=1 parts a-c to find the mean and variance of Ä.

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