Let X and Y each take on either the value 1 or -1. Let

pr(1,1)=pr(X=1, Y=1)

pr(1,-1)=pr(X=1,Y=-1)

pr(-1,1)=pr(X=-1,Y=1)

pr(-1,-1)=pr(X=-1,Y=-1)

Suppose that E[X]=E[Y]=0. Show that

(a)pr(1,1)=pr(-1,-1)

(b)pr(1,-1)=pr(-1,1)

Let p=2p(1,1), Find

(c) Var[X]

(d) Var[Y]

(e) Cov[X,Y]

Ok, I started by making this joint distribution table

But I don't understand parts C, D, and E. What does p=2p(1,1) mean in relation to C, D, and E?

If I ignore the part about p=2p(1,1) I can see that

var[X]=var[Y]=0.5 and that cov[X,Y]=0 because X and Y are independent