Question

Markov Chain Matrix 0 1 0 0.4 0.6 1 0.7 0.3 a.) suppose process begins at...

Markov Chain

Matrix

0 1

0 0.4 0.6

1 0.7 0.3

a.) suppose process begins at state 1 and time =1 what is the probability

it will be at state 0 at t=3.

b.) What is the steady state distribution of the Markov Chain above

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a) Probability of being at state 0 at time 3 has 2 cases

1. Going from 1 to 0 at time 2 and then staying at 0. Probability is 0.7 X 0.4 = 0.28.

2. Staying at 1 at time 2 and then moving to state 0. Probability is 0.3 X 0.7 = 0.21

So, total probability of event is 0.28 + 0.21 = 0.49.

b) Solving

where

We have the following equations

This gives us that

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