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2.11 You start with five dice. Roll all the dice and put aside those dice that come up 6. Then, roll the remaining dice, putting aside those dice that come up 6. And so on. Let X, be the number of dice that are sixes after n rolls. (a) Describe the transition matrix P for this Markov chain. (b) Find the probability of getting all sixes by the third play. (c) What do you expect P00 to look like? Use technology to confirm your answer.

2.11 You start with five dice. Roll all the dice and put aside those dice that come up 6. Then, roll the remaining dice, putting aside those dice that come up 6. And so on. Let X, be the number of dice that are sixes after n rolls. (a) Describe the transition matrix P for this Markov chain. (b) Find the probability of getting all sixes by the third play. (c) What do you expect P00 to look like? Use technology to confirm your answer.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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2.11 You start with five dice. Roll all the dice and put aside those dice that come up 6. Then, roll the remaining dice, putting aside those dice that come up 6. And so on. Let X, be the number of dice that are sixes after n rolls. (a) Describe the transition matrix P for this Markov chain. (b) Find the probability of getting all sixes by the third play. (c) What do you expect P00 to look like? Use technology to confirm your answer.
Transcribed Image Text:2.11 You start with five dice. Roll all the dice and put aside those dice that come up 6. Then, roll the remaining dice, putting aside those dice that come up 6. And so on. Let X, be the number of dice that are sixes after n rolls. (a) Describe the transition matrix P for this Markov chain. (b) Find the probability of getting all sixes by the third play. (c) What do you expect P00 to look like? Use technology to confirm your answer.
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