Let X, Y, Z random variables taking values in {-1,1}.
Suppose X and Z conditionally independent given Y.
Prove that Cov(X,YZ) <= Cov(X,Y) .

Hint: prove that Cov(X,YZ) = a*Cov(X,Y) with a=(E[Z|Y=1]+E[Z|Y=-1])/2 .

I tried, but I'm really not able to do it. Can someone help me?