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Which of the following is/are true for a Markov chain Xk+1 Axk, k = 0, 1,2, ..., where A is an n x n stochastic matrix? (Select all that apply) ✔The sum of each row of A is 1. If A is regular, then A has a unique probability vector that is an eigenvector corresponding to eigenvalue 1. If A is regular, then Ak p approaches the same probability vector for any probability vector p as k approaches infinity. If p is any probability vector, then Ap is a probability vector. If A is regular, then A has 1 as an eigenvalue.

Which of the following is/are true for a Markov chain Xk+1 Axk, k = 0, 1,2, ..., where A is an n x n stochastic matrix? (Select all that apply) ✔The sum of each row of A is 1. If A is regular, then A has a unique probability vector that is an eigenvector corresponding to eigenvalue 1. If A is regular, then Ak p approaches the same probability vector for any probability vector p as k approaches infinity. If p is any probability vector, then Ap is a probability vector. If A is regular, then A has 1 as an eigenvalue.

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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Which of the following is/are true for a Markov chain Xk+1 = (Select all that apply) Axk, k = 0, 1, 2, · · ·, where A is an n x n stochastic matrix? ✔The sum of each row of A is 1. If A is regular, then A has a unique probability vector that is an eigenvector corresponding to eigenvalue 1. If A is regular, then Akp approaches the same probability vector for any probability vector p as k approaches infinity. If p is any probability vector, then Ap is a probability vector. If A is regular, then A has 1 as an eigenvalue.
Transcribed Image Text:Which of the following is/are true for a Markov chain Xk+1 = (Select all that apply) Axk, k = 0, 1, 2, · · ·, where A is an n x n stochastic matrix? ✔The sum of each row of A is 1. If A is regular, then A has a unique probability vector that is an eigenvector corresponding to eigenvalue 1. If A is regular, then Akp approaches the same probability vector for any probability vector p as k approaches infinity. If p is any probability vector, then Ap is a probability vector. If A is regular, then A has 1 as an eigenvalue.
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