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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.
i have attached the homework sheet and i highlighted some question which i could not answer
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