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 .

Thus, .

I do not recognize the density function and its support.

Any help would be great. Not sure where I went wrong.

Thanks