A magical horse offers Jeff Bezos the following game. He starts by paying the horse an entrance fee of one hundred billion dollars. Then a fair coin is flipped until tails appears for the first time, at which point the game ends. He receives a payoff of 2n dollars, where n is the number of times the coin was flipped before the game ended. Let X be the random variable denoting his total gain or loss from this game. Required:
a. Calculate the expectation of X.
b. Explain how you would interpret the result of Part (a) in terms of whether the horse’s offer is in his financial interest.