The transition matrix for a Markov process is given by State State 5 3 State 2 (

Question

The transition matrix for a Markov process is given by State State 5 3 State 2 (a) What does the entry a22 = represent? O The conditional probability that the outcome state 2 will occur given that the outcome state 1 has occurred is 1. O The conditional probability that the outcome state 1 will occur given that the outcome state 2 has occurred is O The conditional probability that the outcome state 1 will occur given that the outcome state 1 has occurred is O The conditional probability that the outcome state 2 will occur given that the outcome state 2 has occurred is 3 3 3 None of these are correct (b) Given that the outcome state 1 has occurred, what is the probability that the next outcome of the experiment will be state 2? (c) If the initial-state distribution is given by State 1 6 State 2 6 find TXo, the probability distribution of the system after one observation

Explanation / Answer

(a) The element a22 represents the condition probability that the outcome state 2 will occur given that the outcome state 2 has occured is 1/3

Correct answer is Option D

(b)

Given state 1 has occured, for the next outcome state 2 to occur it will be given a12, which in the above matrix is having the value of 2/3 or 0.67

(c)

X1 = TXo

=> [1/5 * 1/6 + 2/3 * 5/6, 4/5 * 1/6 + 1/3 * 5/6]

=> [0.588888888, 0.4111111]

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