Suppose we want to know the average (or expected) number of steps it will take to go from state i to state j in a Markov chain. It can be shown that the following computation answers thisquestion: Delete the jth row and the jth column of the transition matrix P to get a new matrix Q. (Keep the rows and columns of Q labeled as they were in P.) The expected number of steps fromstate i to state j is given by the sum of the entries in the column of (I – Q)¯- labeled i.-1Suppose that the weather in a particular region behaves according to a Markov chain. Specifically, suppose that the probability that tomorrow will be a wet day is 0.662 if today is wet and 0.125 iftoday is dry. The probability that tomorrow will be a dry day is 0.875 if today is dry and 0.338 if today is wet.tIf Monday is a dry day, what is the expected number of days until a wet day?days

Given information: In the given Markov model, there are 2 states. A state transition matrix consists…

Suppose we want to know the average (or expected) number of steps it will take to go from state i to state j in a Markov chain. It can be shown that the following computation answers this question: Delete the jth row and the jth column of the transition matrix P to get a new matrix Q. (Keep the rows and columns of Q labeled as they were in P.) The expected number of steps from state i to state j is given by the sum of the entries in the column of (I - Q)-1 labeled i. Suppose that the weather in a particular region behaves according to a Markov chain. Specifically, suppose that the probability that tomorrow will be a wet day is 0.662 if today is wet and 0.125 if today is dry. The probability that tomorrow will be a dry day is 0.875 if today is dry and 0.338 if today is wet.t If Monday is a dry day, what is the expected number of days until a wet day?

Suppose we want to know the average (or expected) number of steps it will take to go from state i to state j in a Markov chain. It can be shown that the following computation answers this question: Delete the jth row and the jth column of the transition matrix P to get a new matrix Q. (Keep the rows and columns of Q labeled as they were in P.) The expected number of steps from state i to state j is given by the sum of the entries in the column of (I - Q)-1 labeled i. Suppose that the weather in a particular region behaves according to a Markov chain. Specifically, suppose that the probability that tomorrow will be a wet day is 0.662 if today is wet and 0.125 if today is dry. The probability that tomorrow will be a dry day is 0.875 if today is dry and 0.338 if today is wet.t If Monday is a dry day, what is the expected number of days until a wet day?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 15EQ

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