# Question

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?

## Answer to relevant Questions

Each night different meteorologists give us the probability that it will rain the next day. To judge how well these people predict, we will score each of them as follows: If a meteorologist says that it will rain with ...If E[X] = 1 and Var(X) = 5, find (a) E[(2 + X)2]; (b) Var(4 + 3X). When coin 1 is flipped, it lands on heads with probability .4; when coin 2 is flipped, it lands on heads with probability .7. One of these coins is randomly chosen and flipped 10 times. (a) What is the probability that the ...In Problem 5, for n = 3, if the coin is assumed fair, what are the probabilities associated with the values that X can take on? Problem 5 Let X represent the difference between the number of heads and the number of tails ...An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently) agrees to be interviewed with probability 2/3, what is the probability that her ...Post your question

0