Let X(1) X(2) ... X(n) be the order statistics for a i.i.d. random...

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Let X(1) ≤ X(2) ≤ ... · ≤X(n) be the order statistics for a i.i.d. random sample X₁, 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. Let X(1) ≤ X(2) ≤ ... · ≤X(n) be the order statistics for a i.i.d. random sample X₁, 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 the full answer