Question: 20. Let F be a distribution function. Prove that the functions Fn and 1 (1 F)n are also distribution functions. Hint: Let X1,X2,

20. Let F be a distribution function. Prove that the functions Fn and 1 − (1 − F)n are also distribution functions.

Hint: Let X1,X2, . . . ,Xn be independent random variables each with the distribution function F. Find the distribution functions of the random variables max(X1,X2, . . . ,Xn) and min(X1,X2, . . . ,Xn).

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