Solve the below:
Q: A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 on the second and in general $2^k if it first appears on the kth toss. Let the random variable X denote our winnings. How much should we pay in order for this to be a fair game.
(a) What if the amounts won are c^k instead of 2^k where 0
(b) the amounts won are log 2^k