Basic Probability Summer 2011
Assignment Two  additional problems
1) Consider the Gamblers Ruin Problem (page 17, Example 1.7.4 for
p
= 1
/
2
and page 74, Example 3.9.6 for case of general
p
.) Let
D
k
denote the average
number of plays it takes for the gambler to either go broke or win, given that
he starts with
k
dollars. In other words, for a random walk with probability
p
of going up one on each step, with absorbing barriers 0 and
N
, what is
the mean number of steps before hitting either of the absorbing barriers,
starting at
k
. (
Hint:
verify equation (8), pg. 74, which is a second order,
linear diﬀerence equation with constant coeﬃcients. There is a link on our
webpage to a succinct tutorial on how to solve such things.)
2) A prisoner is trapped in a cell with three doors. The ﬁrst door leads to a
tunnel that returns him to his cell after two days of travel. The second door
leads to a tunnel that returns him to his cell after three days of travel. The
third door leads immediately to freedom.
a) Assuming that the prisoner will always select doors 1, 2, and 3 with
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 Spring '11
 Thompson
 Algebra, Algebraic Topology, Addition, Probability, Probability theory, Linear Difference Equation, Basic Probability Summer, Gamblers Ruin Problem

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