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
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 03/21/2012 for the course MA 2b taught by Professor Makarov,n during the Winter '08 term at Caltech.