Question: Suppose that F(x) is a cumulative distribution function. Show that (a) Fn(x) and (b) 1 [1 F(x)]n are also cumulative distribution functions when

Suppose that F(x) is a cumulative function. Show that (a) Fn(x) and (b) 1 − [1 − F(x)]n are also cumulative functions when n is a positive integer.

Let X1, . . . ,Xn be independent random variables having the common function F. Define random variables Y and Z in terms of the Xi so that P{Y ≤ x} = Fn(x) and P{Z ≤ x} = 1 − [1 − F(x)]n.

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