37. Let X1, X2,..., Xn be independent random variables, each having a uniform distribution over (0,1). Let

Question:

37. Let X1, X2,..., Xn be independent random variables, each having a uniform distribution over (0,1). Let M = maximum (X1, X2,..., Xn). Show that the distribution function of M, FM (·), is given by FM (x) = xn, 0 ≤ x ≤ 1 What is the probability density function of M?

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