A Markov chain has the transition matrix shown below: 0.3 [0.5 0.2 P = | 0.7 0.3 1 0 0 (Note: For questions 1, 3, and 5, 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 next observation? (2) If, on the first observation the system is in state 1, what state is the system most likely to occupy on the next observation? (If there is more than one such state, which is the first one.) (3) If, on the first observation, the system is in state 1, what is the probability that the system is in state 1 on the third observation? (4) If, on the first observation the system is in state 1, 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.) (5) If, on the first observation, the system is in state 2, what is the probability that on the next four observations it successively occupies states 3, 1, 2, and 1 (in that order)?

A Markov chain has the transition matrix shown below: 0.3 [0.5 0.2 P = | 0.7 0.3 1 0 0 (Note: For questions 1, 3, and 5, 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 next observation? (2) If, on the first observation the system is in state 1, what state is the system most likely to occupy on the next observation? (If there is more than one such state, which is the first one.) (3) If, on the first observation, the system is in state 1, what is the probability that the system is in state 1 on the third observation? (4) If, on the first observation the system is in state 1, 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.) (5) If, on the first observation, the system is in state 2, what is the probability that on the next four observations it successively occupies states 3, 1, 2, and 1 (in that order)?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 3 after three periods is a. 0.259 b. 0.261 c. 0.283 d. 0.296
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The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 2 after two periods is a. 0.283 b. 0.26 c. 0.261 d. 0.47
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