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2. Vito is lost in a maze. At the center of the maze, there are 3 paths. Path 1 leads out of the maze after a 2 minute walk. Paths 2 and 3 lead back to the center of the maze after 2 and 3 minute walks, respectively. Suppose that each time Vito is at the center of the maze he picks path i with probability i/6. Show that, on average, Vito finds his way out in 15 minutes. Hint: Use "First Step Analysis". That is, use the Law of Total Expectation, with respect to his first choice.

2. Vito is lost in a maze. At the center of the maze, there are 3 paths. Path 1 leads out of the maze after a 2 minute walk. Paths 2 and 3 lead back to the center of the maze after 2 and 3 minute walks, respectively. Suppose that each time Vito is at the center of the maze he picks path i with probability i/6. Show that, on average, Vito finds his way out in 15 minutes. Hint: Use "First Step Analysis". That is, use the Law of Total Expectation, with respect to his first choice.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. Vito is lost in a maze. At the center of the maze, there are 3 paths. Path 1 leads out of the maze after a 2 minute walk. Paths 2 and 3 lead back to the center of the maze after 2 and 3 minute walks, respectively. Suppose that each time Vito is at the center of the maze he picks path i with probability i/6. Show that, on average, Vito finds his way out in 15 minutes. Hint: Use "First Step Analysis". That is, use the Law of Total Expectation, with respect to his first choice.
Transcribed Image Text:2. Vito is lost in a maze. At the center of the maze, there are 3 paths. Path 1 leads out of the maze after a 2 minute walk. Paths 2 and 3 lead back to the center of the maze after 2 and 3 minute walks, respectively. Suppose that each time Vito is at the center of the maze he picks path i with probability i/6. Show that, on average, Vito finds his way out in 15 minutes. Hint: Use "First Step Analysis". That is, use the Law of Total Expectation, with respect to his first choice.
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