1. ## independent random variables

Thanks

2. Originally Posted by nerdo

Thanks
(i) Well the joint density is the product of marginal densities, since they are independent. So can you do it now?

(ii) Var(X-Y) = Var(X) + Var(-Y) = Var(X) + Var(Y) = 9 + 1 = 10

The first equality is justified because X and Y are independent.
Why is the second equality justified?

(iii) $E(X^2) = Var(X) + (E(X))^2 = 9 + 2^2 = 13$

(iv) $E(X+Y) = E(X) + E(Y) = 2 - 3 = -1$

3. I know this will sound stupid , but how do i calcaulate the joint density of product of marginal densities. I hav tried for hours but i can not seem to figure it out.

4. Originally Posted by nerdo
I know this will sound stupid , but how do i calcaulate the joint density of product of marginal densities. I hav tried for hours but i can not seem to figure it out.
I don't see the trouble here ....

If X and Y are independent random variables and the pdf of X is f(x) and the pdf of Y is g(y) then the joint pdf of X and Y is given by f(x) g(y).