Aperson tosses a fair coin until a tail appears for the first time. if the tail appears on the n th flip, the person wins 2 n dollars. let x denote the player’s winnings. show that e [ x ] = + [infinity] . this problem is known as the st. petersburg paradox. would you be willing to pay $1 million to play this game once? 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?