I had a similar problem and I was trying to solve this question based on reply (thank you so much!!) but im having a difficult time to do following question:

For Z distributed on R^3 with Z1, Z2, Z3 IID Z ~ exp(1)

If i have W = (Z1 ^2, Z2 ^2, Z1Z2) then how can I find expected value and variance?

Do I still use gamma distribution? I am so confused....

plz help me!!!