When rolling a fair six-sided die, on average, how many flips will it take until the pattern 123123 emerges? Note: modeling this as a Markov chain is seriously overcomplicating things. Each row of the P matrix would be 1/6, 1/6, 1/6, 1/6, 1/6, 1/6. Limiting probabilities would be 1/6 and it would take, on average, 6 transitions to get from any state to any other state. It still fits into a Markov chain framework, which will allow us to find the expected time until the pattern forms. Noto: it doesn't matter which state we start in Represent the initial state (which isn't givzen) as *

When rolling a fair six-sided die, on average, how many flips will it take until the pattern 123123 emerges? Note: modeling this as a Markov chain is seriously overcomplicating things. Each row of the P matrix would be 1/6, 1/6, 1/6, 1/6, 1/6, 1/6. Limiting probabilities would be 1/6 and it would take, on average, 6 transitions to get from any state to any other state. It still fits into a Markov chain framework, which will allow us to find the expected time until the pattern forms. Noto: it doesn't matter which state we start in Represent the initial state (which isn't givzen) as *

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...

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