Question 1) A mouse rans through the maze shown below. At each step it leaves the room it is in by choosing a random one of the doors out of the room. 1 4 a) Give the transition matrix P for this Markov chain. b) Find the stationary probabilities of each stage. c) Now suppose that a piece of cheese is placed on a deadly trap in Room 5. The mouse starts in Room 1. Find the expected number of steps before reaching Room 5 for the first time, starting in Room 1. d) Find the expected time to return to Room 1.

Question 1) A mouse rans through the maze shown below. At each step it leaves the room it is in by choosing a random one of the doors out of the room. 1 4 a) Give the transition matrix P for this Markov chain. b) Find the stationary probabilities of each stage. c) Now suppose that a piece of cheese is placed on a deadly trap in Room 5. The mouse starts in Room 1. Find the expected number of steps before reaching Room 5 for the first time, starting in Room 1. d) Find the expected time to return to Room 1.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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