Suppose that F(x) is a cumulative distribution function. Show that (a) Fn(x) and (b) 1 [1

Question:

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.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...