Question: 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

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.

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Solution a Derivation of the probability distribution of X1 X1 is the smallest order statistic which means that it is the minimum value of the random ... View full answer

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