# squiz3 - Solutions to quiz 3(January 26 1 We are in the...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions to quiz # 3 (January 26) 1. We are in the situation of the asymmetric random walk with the absorbing barriers at x = 0 and x = 3. The particle starts at k = 1, moves one step to the right with probability p = 3 / 5 and one step to the left with probability q = 2 / 5. Hence the probability that it reaches x = 3 before it reaches x = 0 is 1- ( q/p ) 1 1- ( q/p ) 3 = 1- (2 / 3) 1- (2 / 3) 3 = 9 19 . If you forgot the formula, here is a quick way to find the answer. Let x 1 be the probability that A eventually wins if he initially has \$1 and let x 2 be the probability that A eventually wins if he initially has \$2. Then x 1 = (3 / 5) x 2 , since for A to win starting with \$1, he has to win \$1 in the first play and then to win eventually. Similarly, x 2 = (3 / 5) + (2 / 5) x 1 , since for A to win starting with \$2, he can either win in the first play or lose in the first play and then win eventually. From this system of equations we obtain x 2 = (5 / 3) x 1 and (5 / 3) x 1 = (3 / 5) + (2...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online