Consider the following random walk on the "ring" of size 10: the state space is {0, 1, 2, 3, 4, 5, 6, 7, 8,9},and the random walk jumps +3 with probability 1/3, jumps -2 with probability 1/6, andjumps -1 with probability 1/2. (The operations are meant mod 10, so 8 +3 gives 1.)Find a stationary distribution of the Markov chain.Hint: Do not try to solve the equation system, try to look for a special property of theMarkov chain instead.

Given the random walk on the "ring" of size 10 : the state space is {0, 1, 2, 3, 4, 5, 6, 7, 8,9}.…

Answered: Consider the following random walk on…

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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Consider a Markov chain in the set {1, 2, 3} with transition probabilities p12 = p23 = p31 = p, p13 = p32 = p21 = q = 1 − p, where 0 < p < 1. Determine whether the Markov chain is reversible.
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Suppose it is known that in the city of Golden the weather is either "good" or "bad". If the weather is good on any given day, there is a 2/3 chance it will be good the next day. If the weather is bad on any given day, there is a 1/2 chance it will be bad the next day. a) Find the stochastic matrix P for this Markov chain. b) Given that on Saturday there is a 100% chance of good weather in Golden, use the stochastic matrix from part (a) to find the probability that the weather on Monday will be good. The initial state xo = c) Over the long run, what is the probability that the weather in Golden is good?
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