Q: Let by independent, uniformly distributed random variables on the interval . Find the
a) Probability distribution function of .
b) density function of .
c) mean and variance of .
A: If I can figure out a) and identify the pdf, the cdf (part b) and mean / variance (part c) should follow. So, here is my attempt
Let . Then, by Thereom blah, we have
, with .
I do not recognize the density function and its support.
Any help would be great. Not sure where I went wrong.
Just because you can't recognize this, doesn't mean it's wrong.
AND there is only one y, whether you call it or .....
is the derivative of the CDF that CB derived.
If you are curious....
If we let then X is a Beta and you can obtain the mean and variance that way if you wish.