# Question: A person tosses a fair coin until a tail appears

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?

(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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