Question

A coin that when flipped comes up headswith probability p until either heads or tails has occured twice. Find the expected number of flips

Answer 1

Let X be the number of flips , then the probability mass function be X is:
P₂ = p² + (1-p)² = 2p² +1 -2p
And P₃ = 1-P₂ = ( 2p -2p² )
Hence E[X] = 2P₂ + 3P₃ = 3-p² - (1-p)² (Ans)