Here's a homework question:
A coin's probability to land on H is $p$. We toss it until we get the same result as we did the first time. Let $X$ be the number of times we tossed the coin.
What is the expected value of $X$?
Okay so first I have to define the probability mass function (PMF) of $X$, right? My problem is - how do I take into account the result of the first toss?
Also - I read a little and found out about the Pascal PMF of order $k$, which seems suitable for my case. Should I use it?