Let X(1) X(2) ... X(n) be the order statistics for a i.i.d. random sample X, X2, ..., Xn from an exponential distribution with the

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Let X(1) X(2) ... X(n) be the order statistics for a i.i.d. random sample X, X2, ..., Xn from an exponential distribution with the parameter 0. (a) Derive the probability distribution of X(1). (b) Derive the probability distribution of X(n). (c) For random samples of size n = 2m + 1 from this kind of population, derive the probability distribution of the sample median X.