Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Statistics & Exploratory Data Analysis Markov Chains
Consider a Markov Chain with state space {0,1,2,3,4} and transition matrix
P = \(\begin{pmatrix} 1 & 0 & 0 & 0 & 0\\ 1/3 & 1/3 & 1/3 & 0 & 0\\ 0 & 1/3 & 1/3 & 1/3 & 0 \\ 0 & 0 & 1/3 & 1/3 & 1/3\\ 0 & 0 & 0 & 0 & 1 \end{pmatrix}\)
Then \(\lim _{n \rightarrow \infty} p_{23}^{(n)}\) equals
1
\(\frac{1}{3}\)
2
\(\frac{1}{2}\)
3
0
4
1
5
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