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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?

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    Hint: Consider the hypotheses of the first result and apply the formula of total probability. To calculate pmf of $X$ you may better calculate the pmf of the event that $X$ has not occur in $n$ steps.2011-12-01

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