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**puggles** 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 $\displaystyle N$ and $\displaystyle N^2$. Use this to find the variance of $\displaystyle N$.

So, I know how to compute $\displaystyle E[N]$ & $\displaystyle E[N^2]$ 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 $\displaystyle E[N^2]$ via that route. I know I can utilize $\displaystyle E[N^2]=E[E[N^2|Y]]$, but I'm not sure how to solve $\displaystyle E[N^2|Y]$. I think a little nudge in the right direction is all I need! Thanks