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QUESTION 3 Assume that a continuous time Markov chain has four states, 1, 2 3 and 4, and moves from one state to another with the following rates from state 2 to state 4 two tines per hour, and from state 2 to state 3 four times per hour, from state 3 to states 1, 2 and 4 each with the rate of once per hour States 1 and 4 are absorbing, that is, the transition rate out of these states is zero (a) Let r, be the probability that the process is eventually absorbed into state 4, provided that it starts at state 1, for i = 1,2, 3, 4 Find the values r, for z 1,2, 3, 4 (b) Let T, be the average tıme taken untıl absorption into either state 1 or state 4, provided that the = 1,2, 3, 4 process starts at state z Fınd the values T, for z = (c) If the initial state is 3, find the probability that after 4 transıtions the process is at state 3 (d) Prove that the process is always eventually absorbed either into state 1 or into state 4

QUESTION 3 Assume that a continuous time Markov chain has four states, 1, 2 3 and 4, and moves from one state to another with the following rates from state 2 to state 4 two tines per hour, and from state 2 to state 3 four times per hour, from state 3 to states 1, 2 and 4 each with the rate of once per hour States 1 and 4 are absorbing, that is, the transition rate out of these states is zero (a) Let r, be the probability that the process is eventually absorbed into state 4, provided that it starts at state 1, for i = 1,2, 3, 4 Find the values r, for z 1,2, 3, 4 (b) Let T, be the average tıme taken untıl absorption into either state 1 or state 4, provided that the = 1,2, 3, 4 process starts at state z Fınd the values T, for z = (c) If the initial state is 3, find the probability that after 4 transıtions the process is at state 3 (d) Prove that the process is always eventually absorbed either into state 1 or into state 4

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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QUESTION 3 Assume that a continuous time Markov chain has four states, 1, 2 3 and 4, and moves from one state to another with the following rates from state 2 to state 4 two tines per hour, and from state 2 to state 3 four times per hour, from state 3 to states 1, 2 and 4 each with the rate of once per hour States 1 and 4 are absorbing, that is, the transition rate out of these states is zero (a) Let r, be the probability that the process is eventually absorbed into state 4, provided that it starts at state 1, for i = 1,2, 3, 4 Find the values r, for z 1,2, 3, 4 (b) Let T, be the average tıme taken untal absorption into either state 1 or state 4, provided that the process starts at state z Fınd the values T, for z = 1,2, 3, 4 (c) If the initial state is 3, find the probability that after 4 transıtions the process is at state 3 (d) Prove that the process is always eventually absorbed either into state 1 or into state 4
Transcribed Image Text:QUESTION 3 Assume that a continuous time Markov chain has four states, 1, 2 3 and 4, and moves from one state to another with the following rates from state 2 to state 4 two tines per hour, and from state 2 to state 3 four times per hour, from state 3 to states 1, 2 and 4 each with the rate of once per hour States 1 and 4 are absorbing, that is, the transition rate out of these states is zero (a) Let r, be the probability that the process is eventually absorbed into state 4, provided that it starts at state 1, for i = 1,2, 3, 4 Find the values r, for z 1,2, 3, 4 (b) Let T, be the average tıme taken untal absorption into either state 1 or state 4, provided that the process starts at state z Fınd the values T, for z = 1,2, 3, 4 (c) If the initial state is 3, find the probability that after 4 transıtions the process is at state 3 (d) Prove that the process is always eventually absorbed either into state 1 or into state 4
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