Suppose that a Markov chain with 3 states and with transition matrix P is in state 3 on the first observation. Which of the following expressions represents the probability that it will be in state 1 on the third observation? (A) the (3, 1) entry of P (B) the (1,3) entry of P3 (C) the (3,1) entry of P4 (D) the (1,3) entry of P2 (E) the (3, 1) entry of P (F) the (1,3) entry of P4 (G) the (3, 1) entry of P2 (H) the (1,3) entry of P

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.7: Applications
Problem 15EQ
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Suppose that a Markov chain with 3 states and with transition matrix P is in state 3
on the first observation. Which of the following expressions represents the probability
that it will be in state 1 on the third observation?
(A) the (3, 1) entry of P3
(B) the (1,3) entry of P3
(C) the (3, 1) entry of Pª
(D) the (1,3) entry of P2
(E) the (3, 1) entry of P
(F) the (1,3) entry of P4
(G) the (3, 1) entry of P2
(H) the (1,3) entry of P
Transcribed Image Text:Suppose that a Markov chain with 3 states and with transition matrix P is in state 3 on the first observation. Which of the following expressions represents the probability that it will be in state 1 on the third observation? (A) the (3, 1) entry of P3 (B) the (1,3) entry of P3 (C) the (3, 1) entry of Pª (D) the (1,3) entry of P2 (E) the (3, 1) entry of P (F) the (1,3) entry of P4 (G) the (3, 1) entry of P2 (H) the (1,3) entry of P
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