I have four random variables, A, B, C, D, with known mean and variance. As well:
- Cov(A,B) is known and non-zero
- Cov(C,D) is known and non-zero
- A and C are independent
- A and D are independent
- B and C are independent
- B and D are independent
I then create two new random variables:
- X = A*C
- Y = B*D
Is there any way to determine Cov(X,Y) or Var(X+Y)?
If not exactly, is there any way to estimate it? What if I could determine the distributions of A and B and C and D?