MATH 2B WINTER 2012 HOMEWORK 3 DUE MONDAY 1/23 AT NOON All numbered problems are from Pitman. (1) 3.1.10 (2) 3.1.16 (3) 3.2.5 (4) 3.2.14 (5) 3.review.22 (6) (counts as 3 problems) [Gambler’s Ruin] A gambler repeatedly bets a dollar on a sequence of i.i.d. coin tosses. The gambler starts with m dollars, and will stop if he/she either runs out of money or ends up with total of n dollars. Unbeknownst to the gambler, the coin is unfair, and comes up heads with probability p < 1 / 2 (the gambler always bets heads). Let q = 1-p . This problem leads you through an understanding of why they will probably lose all their money, regardless of their wealth. Note that there is a good chance that you will ﬁnd this problem challeng-ing. You don’t need anything beyond math 1a and basic rules of expected value, etc; however, the combination tends to be confusing. We intend to be generous with partial credit. (a) Let
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