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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 P100 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 P100 to look like? Use technology to confirm your answer.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 P100 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 P100 to look like? Use technology to confirm your answer.
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