hi! can anyone teach me how to prove the following?
E(X^2)= (E(x))^2 + Var X
and
Cov((aX + bZ), Y) = aCov(X, Y) + bCov(Z,Y)
Hi - I would suggest you try it out for yourself. It is pretty straight fwd.
I will get you started. Cov(XV) = E((X-E(X)(Y-E(Y)) - This is the definition and your starting point
In this put X = aX+bZ and simplify the expression. Thats all there is to this prove
Hope you know that E(aX+bZ) = aE(X) + bE(Z)
If not try prove this first.
This has nothing to do with expanding!
If you had A = B - C I would hope that at this level you could make B the subject. This is basic algebra. If you honestly cannot do this you have absolutely no business attempting questions like the one you posted.