I have a faked coin and I throw it until I first get a head H.
$X=1$ for H with prob. $p$
$X=0$ for T with prob. $1-p$
I am a little bit confused right now with two things:
What is the probability that the experiment (after finite time) will end?
Let $N$ be the number of tails until the first time head appears. What is the probability distribution for the random variable N ?