Question

A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.
(a) If the initial distribution for states A, B, and C is P0 = ( 1／3 , 1／3 , 1／3 ), find the distribution of X2

(b) Find the steady state distribution by solving πP = π.

Answer 1

Answer:

A) distribution of x2 = ( 0.4167 0.25 0.3333 )

B) steady state distribution = $\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}$

Step-by-step explanation:

Hello attached is the detailed solution for problems A and B

A) distribution states for A ,B, C:

Po = ( 1/3, 1/3, 1/3 )  we have to find the distribution of x2 as attached below

after solving the distribution

x 2 = ( 0.4167, 0.25, 0.3333 )

B ) finding the steady state distribution solving

$\pi p = \pi$

below is the detailed solution and answers