You have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 9 (inclusive). If the digit is a one, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday. (a) Use the states (1) employed by the DAA and (2) not employed by the DAA to set up the transition matrix P for the system with decimal entries.

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 have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 9 (inclusive). If the digit is a one, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday.

(a) Use the states (1) employed by the DAA and (2) not employed by the DAA to set up the transition matrix P for the system with decimal entries.
 
Calculate P2.
 
Calculate P3.
 
(b) What is the probability that you will still be employed by the DAA after each of the next three weeks?
 
What are your long-term prospects for employment at the DAA? 
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