Let X1, X2, . . . , Xn be independent continuous random

Chapter , Problem 72

(choose chapter or problem)

Let \(X_1, X_2, \ldots , X_n\) be independent continuous random variables each with cumulative distribution function F. Show that the joint cdf of \(X_{(1)}\) and \(X_{(n)}\) is

\(F(x, y)=F^{n}(y)-[F(y)-F(x)]^{n}, \quad x \leq y\)

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