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GATE 2020 ST – Question 28

Stochastic Processes · Markov Chains · 1 mark · Numerical answer

A Markov chain on{0,1} has $$P=\begin{pmatrix}1/2&1/2\\1/3&2/3\end{pmatrix}$$ and P(X₀=0)=1/3. Find27E[X₂] (two decimals).

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Correct answer: 16.25 to 16.25

Explanation

Initial state probabilities are(1/3,2/3). After one step P(X₁=1)=1/6+4/9=11/18. After the next, P(X₂=1)=(7/18)(1/2)+(11/18)(2/3)=65/108. For a0–1 variable expectation equals its probability of1. Thus27E[X₂]=65/4=16.25.

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