30. A person tosses a fair coin until a tail appears for the first time. If the...
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30. 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 2" dollars. Let X denote the player's winnings. Show that E[X]+. This problem is known as the St. Peters- burg 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?
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