23. Suppose that F(x) is a cumulative distribution function. Show that (a) F(x) and (b) 1 -...
Question:
23. Suppose that F(x) is a cumulative distribution function. Show that
(a) F(x)
and
(b) 1 - [1 - F(x)]n are also cumulative distribution functions when n is a positive integer.
HINT: Let X1, . . ., Xn be independent random variables having the common distribution function F. Define random variables Y and Z in terms of the Xi, so that P(Y ≤ x) = F(x), and P(Z ≤ x) = 1 - [1 - F(x)]n.
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