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Consider a Markov chain on (1,2) with the given transition matrix P shown below. Use two methods to find the probability that, in the long run, the chain is in state 1. First, raise P to a high power. Then directly compute the steady-state vector. P= 0.9 0.2 0.1 0.8 Raise P to a high power. For the purposes of this solution, raise P to the 100th power. p100- (Type an integer or decimal for each matrix element. Round to five decimal places as needed.)

Consider a Markov chain on (1,2) with the given transition matrix P shown below. Use two methods to find the probability that, in the long run, the chain is in state 1. First, raise P to a high power. Then directly compute the steady-state vector. P= 0.9 0.2 0.1 0.8 Raise P to a high power. For the purposes of this solution, raise P to the 100th power. p100- (Type an integer or decimal for each matrix element. Round to five decimal places as needed.)

A First Course in Probability (10th Edition)
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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- Consider a Markov chain on {1,2} with the given transition matrix P shown below. Use two methods to find the probability that, in the long run, the chain is in state 1. First, raise P to a high power. Then directly compute the steady-state vector. P= 0.9 0.2 0.1 0.8 Raise P to a high power. For the purposes of this solution, raise P to the 100th power. p100 (Type an integer or decimal for each matrix element. Round to five decimal places as needed.)
Transcribed Image Text:- Consider a Markov chain on {1,2} with the given transition matrix P shown below. Use two methods to find the probability that, in the long run, the chain is in state 1. First, raise P to a high power. Then directly compute the steady-state vector. P= 0.9 0.2 0.1 0.8 Raise P to a high power. For the purposes of this solution, raise P to the 100th power. p100 (Type an integer or decimal for each matrix element. Round to five decimal places as needed.)
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