A quarter is bent so that the probabilities of heads and tails are 0.40 and 0.60. If it is tossed twice, what is the covariance of Z, the number of heads obtained on the first toss, and W, the total number of heads obtained in the two tosses of the coin?
I noticed first they're clearly not independent so the covariance is not 0.
I calculated the marginal PMF's of Z and W and their expected values. I know Cov(Z,W) = E(ZW) - E(Z)E(W) but I can't calculate E(ZW) without the joint PMF. If I could recover the joint PMF from the marginals I could procede but from from what I've read that's only possible in certain cases.
I'm stuck, anyone have some hints for me?