Let be independent discrete random variables with E[X]=2, E[Y]=0, E[Z]=0, E[X^2]=20, E[Y^2]=E[Y^2]=16, and Var(X)=Var(Y)=Var(Z)= 16. Let A=X(Y+Z) and B=XY.

Question

Let  be independent discrete random variables with E[X]=2, E[Y]=0, E[Z]=0, E[X^2]=20, E[Y^2]=E[Y^2]=16, and Var(X)=Var(Y)=Var(Z)= 16. Let A=X(Y+Z) and B=XY.
1.Find E[B].
2.Find Var(B).
3.Find E[AB].
4. are A and B independent?
5.Are A and B are conditionally independent, given X=0.
6.Are A and B are conditionally independent, given X=1.

Divine · Answer

sorry i missed the notation of variable at the beginning. Let X,Y,Z be independent discrete random variables cntd..