Hello,

(a) is ... weird Oo

First thing : if X and Y are independent, you can write the product

if not, you have to find the joint pdf of X and Y.

Second thing :

The whole formula is not very correct...

Assuming they're independent :

For the boundaries in (*), that's using the fact that

and that for any measurable function h, if X and Y are independent.*

erm... good luck

How did you get your equality (a) ?