I'm in a university-level probability course and I'm stuck on a homework problem. Currently we are working on multivarate probability distributions. I have this problem: In an earlier exercise, we considered two individuals who each tossed a coin until the first head appeared. Let Y1 and Y2 denote the number of times that persons A and B toss the coin, respectively. If heads occurs with probability p and tails occurs with probability q=1-p, it is reasonable to conclude that Y1 and Y2 are independent and that each has a geometric distribution with parameter p. Consider Y1-Y2, the difference in the number of tosses required by the two individuals. I need to find a lot of information about the experiment, like E(Y1), E(Y2), E(Y1-Y2), etc. I think I can determine all of the other information if I can just find what E(Y1) and E(Y2) are. This problem is different from all the others we've done since it does not give the joint probability density function. Thus, I have no idea where to start. What is the joint probability density function and what are E(Y1) and E(Y2)? I would guess that E(Y1) and E(Y2) simply equal (1/p) [from geometric distribution], but these seem horribly wrong. Any help would be greatly appreciated.