The pair of random variables (X, Y) is equally likely to take any of the four pairs of values (0,1), (1,0), (−1,0), (0,−1). Note that X and Y each have zero mean.

a) Find E[XY].
E[XY]=
b) YES or NO: For this pair of random variables (X, Y), is it true that Var(X+Y)=Var(X)+Var(Y)?

Select an option Yes No
c) YES or NO: We know that if X and Y are independent, then Var(X+Y)=Var(X)+Var(Y). Is the converse true? That is, does the condition Var(X+Y)=Var(X)+Var(Y) imply independence?

Select an option Yes No