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Suppose that the time to death X has an exponential distribution with hazard rate and that...

Suppose that the time to death X has an exponential distribution with hazard rate and that the right-censoring time C is exponential with hazard rate
. LetT min(X,C) and 1 ifX C;0 ,if X C. Assume that X and C are independent. (a) Find P( 1) (b) Find the distribution of T. (c) Show that and T are independent. (d) Let (T1, 1),...,(Tn, n) be a random sample from this model. Show that the maximum likelihood estimator of is n i1 i n i1 Ti. Use parts a–c to nd the mean and variance of ˆ .

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