A Markov chain has the transition matrix shown below: 0.8 0.2 P = 0.3 0.7] (Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second observation? ... ... ... (2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation? ... (3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation? (If there is more than one such state, which is the first one.) ... ...

A Markov chain has the transition matrix shown below: 0.8 0.2 P = 0.3 0.7] (Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second observation? ... ... ... (2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation? ... (3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation? (If there is more than one such state, which is the first one.) ... ...

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 18EQ

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