# assignment_two_addendum - Basic Probability Summer 2011...

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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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assignment_two_addendum - Basic Probability Summer 2011...

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