If X and Y are independent r.v, both uniformly distributed on (0, 1).

Given that

we obtain

For , we have

For , we have

How do I determine the two upper and lower bounds?

Such as for this case we are using: and ??

Another question:

Given joint density of X and Y:

In order to find the density function of X, I meet the same problem:

for x>0,

for x<0,

Why the two different lower bounds?