Grinstead-Snell-Probability · Problem 6.3.27

Sums of Random Variables

Mathematics · expected-value-games

Problem

(from Hamming) A game is played as follows: A random number XX is chosen uniformly from [0,1][0, 1]. Then a sequence Y1,Y2,…Y_1, Y_2, \ldots of random numbers is chosen independently and uniformly from [0,1][0, 1]. The game ends the first time that Yi>XY_i > X. You are then paid (i−1)(i - 1) dollars. What is a fair entrance fee for this game?

Related theory

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