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I got this tutorial question and I had no clue about how to prove this:

Let $\,F(x)\,$ be a distribution function and $\,r\,$ a positive integer.

Show that $\,F(x)^r\,$ is also a distribution function

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Hint: Which properties qualify a function $G:\mathbb R\to\mathbb R$ to be a distribution function? –  Did Sep 23 '12 at 12:35
    
Thanks ! Its non-decreasing. F(-infinity) = 0 and F(infinity) = 1. These still hold when exponentiated if r is positive. This was pretty obvious - I was being stupid –  user929404 Sep 23 '12 at 12:43
    
These are not sufficient to guarantee that F is a distribution function. There is still one more property... –  Did Sep 23 '12 at 12:44
    
@did I remember similar story from another previous question) –  Seyhmus Güngören Sep 23 '12 at 13:05
1  
hope you were referring to continuous from the right –  user929404 Sep 23 '12 at 18:20

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Community answer:

Hint: Which properties qualify a function $G:\mathbb R\to\mathbb R$ to be a distribution function? – did

It's non-decreasing. $F(-\infty) = 0$ and $F(\infty) = 1$. These still hold when exponentiated if $r$ is positive. – user929404

These are not sufficient to guarantee that F is a distribution function. There is still one more property... – did

continuous from the right - user929404

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