We flip a a biased coin 100 times.
p=probability of head
q=1-p= probability of tail.
Let us call the longest run of heads LH and the longest run of tails LT.
We define a random variable X=min(LT,LH) and Y=LH+LT.
What are the probability laws of X and Y?
Thank you for any help.
Ps : It is not a homework.