Hi,
Ive been given this question but i just can figure it out.
Suppose X,Y are Norm(1,1) and are independently and identically distributed.
Find the distribution of :
U =
Any help would be really appreciated.
I'll get you started with a possible approach:
1. You know the joint pdf of X and Y, f(x,y).
2. Consider the cdf of U.
3. if and if so there are two cases to consider.
Case 1: .
Case 2: .
Therefore:
.
Now integrate f(x, y) over the required regions and calculate each term.
4. The pdf of U is given by .