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.