PS please answer all four parts Stochastic matrices Consider

PS: please answer all four parts

Stochastic matrices: Consider the matrix: phi =[0.1 0.2 0.7 0 0 1 0.5 0.5 0] Show that phi is a stochastic matrix. Is phi periodic? Is phi irreducible? Does phi have a unique stationary distribution?

Solution

a) yes it is   because sum of each row is 1

b) the chain is aperiodic. Hence, the period of state 2 divides both 2 and 3, and so the period of state 2 is 1. Since the chain is irreducible, all states are aperiodic.

c) yes it is , reason is same .because a is not 0