Let and be independent and uniformly distributed over the interval . Find . The solution is 0.5.
Originally I thought it was:
but this doesn't seem to right. If anybody has any input, it would be greatly appreciated.
The key is to know that if and are i.i.d. random variables with density function f(y) then the joint density function of and is
for
and zero elsewhere. I can prove this result if you want, but you should have a copy of the proof somewhere.
For your problem for and .
Then .