Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Markov Chains
Consider a homogeneous Markov chain with state space {0, 1, 2} and transition probability matrix (TPM) given by
Let \(P^{(n)}=\left(\left(P_{i j}^{(n)}\right)\right)\) be the n-step TPM. Then which of the following statements is true?
1
\(\displaystyle \lim _{n \rightarrow \infty} P_{21}^{(n)}=1\)
2
The unique stationary distribution of the chain is given by \(\left(\frac{1}{2}, \frac{1}{2}, 0\right)\)
3
{1, 2} forms a closed set of states
4
\(\displaystyle\lim _{n \rightarrow \infty} P_{22}^{(n)}=1\)