A person tosses a fair coin until a tail appears for the first time. If the tail appears on the nth flip, the person wins 2n dollars. Let X denote the player’s winnings. Show that E[X] = +∞. This problem is known as the St. Petersburg paradox.
(a) Would you be willing to pay $1 million to play this game once?
(b) Would you be willing to pay $1 million for each game if you could play for as long as
you liked and only had to settle up when you stopped playing?