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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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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.
 Winter '08
 Makarov,N
 Math, Statistics, Probability

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