Find the cdf of the following rv s the maximum of n iid, Advanced Statistics

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Find the cdf of the following rv s the maximum of n iid

Let X be a rv with CDF FX (x). Find the CDF of the following rv s.

(a) The maximum of n IID rv s, each with CDF FX (x).
(b) The minimum of n IID rv s, each with CDF FX (x).
(c) The difference of the rv s defined in (a) and (b); assume X has a density fX (x). Hint: Let M+ and M- be the maximum and minimum respectively of the Xi. First, conditional on X1 = x, find the joint probability that X1 = M+ and M+ - M- ≤ r.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

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Advanced Statistics: Find the cdf of the following rv s the maximum of n iid

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