Here's the problem I'm working with, what I'm stumped on is below:
A biased coin has probability p of coming up Heads. The coin is tossed repeatedly. Let N be the number of tosses until Heads appears for the first time. By conditioning on the outcome of the first toss, find the expected values of and . Use this to find the variance of .
So, I know how to compute & here without conditioning on the first toss (i.e. I know what the answers are), but I'm a little stumped on how to get via that route. I know I can utilize , but I'm not sure how to solve . I think a little nudge in the right direction is all I need! Thanks