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A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting e never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is choose one of the other programs the following week. If she watches a reality show one week, then she is 4 times a comedy as a sports program the next week. If she watches a sports program one week, then she is 3 times as likely as a reality show the next week. 1. Find the transition matrix for this Markov chain. 1/2 1/2 4/5 1/5

A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting e never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is choose one of the other programs the following week. If she watches a reality show one week, then she is 4 times a comedy as a sports program the next week. If she watches a sports program one week, then she is 3 times as likely as a reality show the next week. 1. Find the transition matrix for this Markov chain. 1/2 1/2 4/5 1/5

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
ChapterCSR: Contents Of Student Resources
Section: Chapter Questions
Problem 11.22EP
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A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting event. This student never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is equally likely to choose one of the other programs the following week. If she watches a reality show one week, then she is 4 times as likely to watch a comedy as a sports program the next week. If she watches a sports program one week, then she is 3 times as likely to watch a comedy as a reality show the next week. 1. Find the transition matrix for this Markov chain. 1/2 1/2 4/5 1/5 3/4 1/4 2. Suppose this student's friends estimate that she is four times as likely to watch a comedy as a reality show and that she will not be watching a sporting event. Find the probability vector representing this estimation. 4/5 1/5 3. What is the probability that she watches a sporting event two weeks from now? 23/40 4. What is the probability that she watches a comedy three weeks from now? 61/200
Transcribed Image Text:A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting event. This student never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is equally likely to choose one of the other programs the following week. If she watches a reality show one week, then she is 4 times as likely to watch a comedy as a sports program the next week. If she watches a sports program one week, then she is 3 times as likely to watch a comedy as a reality show the next week. 1. Find the transition matrix for this Markov chain. 1/2 1/2 4/5 1/5 3/4 1/4 2. Suppose this student's friends estimate that she is four times as likely to watch a comedy as a reality show and that she will not be watching a sporting event. Find the probability vector representing this estimation. 4/5 1/5 3. What is the probability that she watches a sporting event two weeks from now? 23/40 4. What is the probability that she watches a comedy three weeks from now? 61/200
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