Čonsider a 4-state Markov chain (X, : t = 0, 1, 2, 3, ..) with state space S = (1, 2, 3, 4) and probability matrix |0.3 0.2 0.5 0.1 0.2 0.4 0.3 P = 0.6 0.4 0.5 0.4 0.1 If the Markov chain at t = 0,1 goes through states X, = 1 and X1 = 3, what is the probability that it will move to state "2" in the next step (at t = 2). Answer = If the Markov chain at t = 0 is in state X, = 1, what is the probability that it will move to state "3" in the next step (at t = 1) and state "2" after that (at t = 2)? Answer=

Čonsider a 4-state Markov chain (X, : t = 0, 1, 2, 3, ..) with state space S = (1, 2, 3, 4) and probability matrix |0.3 0.2 0.5 0.1 0.2 0.4 0.3 P = 0.6 0.4 0.5 0.4 0.1 If the Markov chain at t = 0,1 goes through states X, = 1 and X1 = 3, what is the probability that it will move to state "2" in the next step (at t = 2). Answer = If the Markov chain at t = 0 is in state X, = 1, what is the probability that it will move to state "3" in the next step (at t = 1) and state "2" after that (at t = 2)? Answer=

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 best describes the long-run probabilities of a Markov chain {Xn: n = 0, 1, 2, ...}? O the probabilities of eventually returning to a state having previously been in that state O the fraction of time the states are repeated on the next step O the fraction of the time being in the various states in the long run O the probabilities of starting in the various states • Previous Not saved Simpfun
1. A Markov chain has state space {0, 1, 2} and transition probability matrix .1 .5 .4 P = 0 0 1 .2 .3 .5 (a) the probability of going from state 0 to state 2 in 2 transitions (b) the steady-state distribution, if it exists Determine:
5
A path of length k in a Markov chain {X,,n= 0,1,...} is a sequence of states visited from step n to step n+k. Let pij be the transition probability from state i to state j. Show that starting from state i,, the probability that the chain follows a particular path i, - i„.1 - in2 - ... - i,t is given by %3D "x*\":= "X)d = i2.,Xpsk = inrk | X, = i,) n+1 n+l> n+2 n+k = P Pu.