answer all parts for exercise 9.2.4 and show all work. se 92.3 The tranobability

Question

answer all parts for exercise 9.2.4 and show all work.

se 92.3 The tranobability matrix of a discre obability matrix of a discrete-time Markov chain is given by 'e random ote by Y, and buted, and are s an alternating r interest with at the process associating a 0 0 0 1.0 0 0 1.0 0 0 P=10001.0 0 0 0.8 0.2 00 0.4 0 0.6 0 0 w all sample paths of length 4 that begin in state 1. What is the probability of being in each of the states1 hrough 5 after four steps beginning in state 1? Evercise ransition probability matrix is given by 9.2.4 Consider a discrete-time Markov chain consisting of four states a, b, c, and d and whose own. As soon tioning state s the random orresponding ribed above, 0.0 0.0 1.0 0.0 0.0 0.4 0.6 0.0 0.8 0.0 0.2 0.0 0.2 0.3 0.0 0.5 ime that the emachine is Compute the following probabilities 9.2.5 at time step n, n A Markov chain with two states a and b has the following conditional probabilities: If it is in . 1,2, ..., then it stays in state a with probability 0.5(0.5)". If it is in state b at 0

Explanation / Answer

a) The required probability here is computed as:

The path here is: a --> c --> c --> c --> c

Probability = 1*0.2*0.2*0.2 = 0.008

Therefore 0.008 is the required probability here.

b) The path here is given as:

a --> b --> c --> d

Probability = 0 because we cannot go from state a to state b in one time step as we can see from the above matrix.

Therefore 0 is the required probability here.

c) The math here given is:

b --> c --> a --> c --> c

Probability = 0.6*0.8*1*0.2 = 0.096

Therefore 0.096 is the required probability here.

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