Here's a question I got for homework:
In every single time unit, Jack and John are tossing two different coins with P1 and P2 chances for heads. They keep doing so until they get different results. Let X be the number of tosses. Find the pmf of X (in discrete time units). What kind of distribution is it?
Here's what I have so far: In every round (time unit) the possible results
HH - p1p2 TT - q1q2 TH - q1p2 HT - q2p1
P(X=k) = ((p1p2 + q1q2)^(k-1))*(q1p2+q2p1)
Which means we're dealing with a geometric distribution.
What doesn't feel right is that the question mentions 'discrete time units'. That makes me think about a Poisson distribution, BUT - Poisson is all about number of successes in a time unit, while here we only have one round in every time unit.
If I'm not too clear its only because I'm a little confused myself. Any hint would be perfect. Thanks in advance