List of top Statistics Questions on Stochastic Processes

Consider a Markov Chain with state space \(S = \{0, 1\}\) and the transition probability matrix \(P = \begin{pmatrix} 1 & 0 \\ 0.5 & 0.5 \end{pmatrix}\). What is the value of \(P^{(2)}_{10}\)?

Consider a Markov Chain with transition probability matrix \(P = \begin{pmatrix}0 & 1 & 0\\0.5 & 0 & 0.5\\0 & 1 & 0\end{pmatrix}\) with state space \(S=\{0,1,2\}\). Then:

Which of the following is essential for completely specifying a Markov Chain?