23.(10 pts) Answer the following using this transitional Markov matrix 0.2 0.3 0

Question

23.(10 pts) Answer the following using this transitional Markov matrix 0.2 0.3 0.5 0.1 0.9 0.0 0.4 0.1 0.5 0.1745 0.6422 0.1833 P10 0.1619 0.6816 0.1566 0.1779 0.6316 0.1905 a. If you are in state 1, what is the probability that after the next transition, you will be in state 1: b. If you are in state 1, what is the probability that after the next transition, you will be in state 2 c. If you are in state 1, what is the probability that after 10 transitions, you will be in state 1: d. If you are in state 1, what is the probability that after 10 transitions, you will be in state 2:

Explanation / Answer

a) Here we use the one step transition matrix as:

p11 = This is the first value of the first row, therefore, we get from the first matrix that:

p11 = 0.2

Therefore 0.2 is the required probability here.

b) The required probability here is computed as:

p12 = 0.3

Therefore 0.3 is the required probability here.

c) Here, we look at the second matrix to get the probabiltiy as:

p11 = 0.1745

Therefore 0.1745 is the required probability here.

d) Here, we look at the second matrix to get the probabiltiy as:

p12 = 0.6422

Therefore 0.6422 is the required probability here.

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