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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?2012-09-23
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    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 stupid2012-09-23
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    These are not sufficient to guarantee that F is a distribution function. There is still one more property...2012-09-23
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    @did I remember similar story from another previous question)2012-09-23
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    @SeyhmusGüngören Do you? :-))2012-09-23
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    @did of course))2012-09-23
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    hope you were referring to continuous from the right2012-09-23

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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