You are submitting a petition that needs to be approved by the Department Chair, the Associate Dean and the Dean. The Department Chair will approve it with probability 80%. Otherwise, he will ask you to make changes and bring it back the next day. The Associate Dean will approve a petition that was previously approved by the Chair with probability 40%. Otherwise, she will ask you to make changes and bring it back to the Chair the next day. Finally, the Dean will approve the petition that was approved by Associate Dean with probability 95%, otherwise sending you back to get approval from the Chair (and then the Associate Dean) the next day. When the petition is approved by one person, you can then take it to the next level the next day. You are interested in evaluating the average time to obtain approvals. i. Model the progress of the petition as a Markov chain. ii. Write down transition matrix, matrices Q and R and calculate matrix N iii. Find the average time to obtain approval

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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You are submitting a petition that needs to be approved by the Department Chair, the Associate Dean and the Dean. The Department Chair will approve it with probability 80%. Otherwise, he will ask you to make changes and bring it back the next day. The Associate Dean will approve a petition that was previously approved by the Chair with probability 40%. Otherwise, she will ask you to make changes and bring it back to the Chair the next day. Finally, the Dean will approve the petition that was approved by Associate Dean with probability 95%, otherwise sending you back to get approval from the Chair (and then the Associate Dean) the next day. When the petition is approved by one person, you can then take it to the next level the next day. You are interested in evaluating the average time to obtain approvals.

i. Model the progress of the petition as a Markov chain.

ii. Write down transition matrix, matrices Q and R and calculate matrix N

iii. Find the average time to obtain approval

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