Let X,Y,Z be independent discrete random variables with

Question

E[X]=2, E[Y]=0, E[Z]=0,
E[X^2]=20
E[Y^2]= E[Z^2]=16,
and
Var(X)=Var(Y)=Var(Z)=16.
Let A=X(Y+Z) and B=XY.
1. Find E[B].
E[B]= ?

2. Find Var(B).
Var(B)= ?

3. Find E[AB].
E[AB]= ?

4. Find Var (B|X = 2)