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 four times 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. (Note: Express your answers as rational fractions or as decimal fractions rounded to 4 decimal places (if the answers have more than 4 decimal places).) (1) Find the transition matrix for this Markov process. P = (2) Find the three-step transition matrix P(3) P(3) = (3) If the student is absent on a given Friday afternoon, what is the probability that he will be present 3 weeks later?
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 four times 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. (Note: Express your answers as rational fractions or as decimal fractions rounded to 4 decimal places (if the answers have more than 4 decimal places).) (1) Find the transition matrix for this Markov process. P = (2) Find the three-step transition matrix P(3) P(3) = (3) If the student is absent on a given Friday afternoon, what is the probability that he will be present 3 weeks later?
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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![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 four times 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.
(Note: Express your answers as rational fractions or as decimal fractions rounded to 4 decimal places (if the answers have more than 4 decimal places).)
**(1) Find the transition matrix for this Markov process.**
\[
P = \begin{bmatrix}
\boxed{\phantom{0}} & \boxed{\phantom{0}} \\
\boxed{\phantom{0}} & \boxed{\phantom{0}}
\end{bmatrix}
\]
**(2) Find the three-step transition matrix \( P(3) \).**
\[
P(3) = \begin{bmatrix}
\boxed{\phantom{0}} & \boxed{\phantom{0}} \\
\boxed{\phantom{0}} & \boxed{\phantom{0}}
\end{bmatrix}
\]
**(3) If the student is absent on a given Friday afternoon, what is the probability that he will be present 3 weeks later?**
\[
\boxed{\phantom{0}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac73edbf-297f-4aed-9f9e-4c41e8d7aed8%2Fe5909cdc-6e43-4343-9a85-55cd7b5ad1ba%2Fxoc89y7_processed.png&w=3840&q=75)
Transcribed Image Text: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 four times 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.
(Note: Express your answers as rational fractions or as decimal fractions rounded to 4 decimal places (if the answers have more than 4 decimal places).)
**(1) Find the transition matrix for this Markov process.**
\[
P = \begin{bmatrix}
\boxed{\phantom{0}} & \boxed{\phantom{0}} \\
\boxed{\phantom{0}} & \boxed{\phantom{0}}
\end{bmatrix}
\]
**(2) Find the three-step transition matrix \( P(3) \).**
\[
P(3) = \begin{bmatrix}
\boxed{\phantom{0}} & \boxed{\phantom{0}} \\
\boxed{\phantom{0}} & \boxed{\phantom{0}}
\end{bmatrix}
\]
**(3) If the student is absent on a given Friday afternoon, what is the probability that he will be present 3 weeks later?**
\[
\boxed{\phantom{0}}
\]
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