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
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
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