Transformation in Math | Definition, Types & Examples

SOLVED: Consider a DTMC with state space 0, 1, 2, 3 and transition probability matrix:| | 0 | 1 | 2 | 3 ||—|—–|—–|—–|—–|| 0 | 1/3 | 2/3 | 0 | 0 || 1 | 1/2 | 0 | 1/2 | 0 || 2 | 0 | 1/2 | 0 | 1/2 || 3 | 0 | 0 | 2/3 | 1/3 |(a) Find the period of this chain:(b) Are the limiting probabilities and the long-run proportions of the time the DTMC in each state the same for this chain? Why or why not? You do not need to compute those probabilities.

SOLVED:A transition probability matrix 𝐏 is said to be doubly stochastic if the sum over each column equals one; that is, ∑i PU=1, for all If such a chain is irreducible and aperiodic and consists of M 1 states 0,1, …, M, show that the limiting probabilities are given by πj=(1)/(M 1), j=0,1, …, M