If the student attends class on a certain Friday, then they are three times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then they are twice as likely to attend class the next Friday as to be absent again.Assume that state 1 is Attends Class and that state 2 is Absent from Class.Find the transition matrix for this Markov process. \( P = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix} \).

Let Si, i=1,2 denote the state i, where state 1 is Attends Class and state 2 is Absent from class. Let Tij denote the transition from Sj to Si. Then the transition probabilities are given as follows: The probability of transition from S1 to S1 be say, Prob(T11)=p Then, the probability of transition from S1 to S2 is Prob(T21)=3p The probability of transition from S2 to S2 be say, Prob(T22)=q Then, the probability of transition from S2 to S1 is, Prob(T12)=2qWe must have, Prob(T11)+Prob(T21)=1 and Prob(T12)+Prob(T22)=1 i.e., p+3p=12q+q=1 This gives, p=14q=13Then, Prob(T21)=3p=3×14=34Prob(T12)=2q=2×13=23 So, the transition matrix for this Markov process is, P=14233413

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If the student attends class on a certain Friday, then he is three times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then he is twice as likely to attend class the next Friday as to be absent again. Assume that state 1 is Attends Class and that state 2 is Absent from Class. Find the transition matrix for this Markov process. P =

If the student attends class on a certain Friday, then he is three times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then he is twice as likely to attend class the next Friday as to be absent again. Assume that state 1 is Attends Class and that state 2 is Absent from Class. Find the transition matrix for this Markov process. P =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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