St. Petersburg problem (or paradox?). How much would you be wilIing to pay to play the following game of chance. A fair coin is tossed by the player until heads appears. If heads appears on the first toss, the bank pays the player 1 dollar. If heads appears for the first time on the second throw the bank pays the player 2 dollars. If heads appears for the first time on the third throw the player receives 4 = 22 dollars. In general, if heads appears for the first time on the nth throw, the player receives 2n - 1 dollars. The amount of money the player will win in this game is a random variable; find its mean. Would you be willing to pay this amount to play the game? (For a discussion of this problem and why it is sometimes called a paradox see T. C. Fry, Probability and Its Engineering Uses, Van Nostrand, New York, 1928, pp. 194-199.)