Let X and Y be independent normal variables, with EX =1 SD(X) = 3, EY = 2, SD(Y) = 4. Let U = X-Y, V = X+ 2Y.?

Question

Find E(V|U)
Find Var(V|U)

Any help would be great! Thanks

Answer 1

I'm not sure what you mean by V|U; the | symbol is normally used for conditional probability, which doesn't make sense here. I'll assume you're just using it as a shortcut to indicate that you want E(V), E(U), Var(V) and Var(U).

Note that E(A+B) = E(A) + E(B) and E(kA) = kE(A).

E(U) = E(X-Y) = E(X) - E(Y) = -1.
E(V) = E(X+2Y) = E(X) + 2E(Y) = 5.

Note that Var(A+B) = Var(A) + Var(B) if A and B are independent, and Var(kA) = k^2 Var(A).

Var(U) = Var(X-Y) = Var(X) + (-1)^2 Var(Y) = 9 + 16 = 25.
Var(V) = Var(X+2Y) = Var(X) + 2^2 Var(Y) = 9 + 64 = 73.

Answer 2

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