Question

You are given a transition matrix P. Find the steady-state distribution vector. HINT [See Example 4.]

A) P =

	5/6	1/6
	7/9	2/9

B) P =

	1/5	4/5	0
	5/8	3/8	0
	4/7	0	3/7

Answer 1

a) Let the steady state vector for the 2 states here be X and Y respectively.

From first column, we have here:
X = (5/6)X + (7/9)Y
X/6 = 7Y/9
X = 14Y/3

Also, we know here that:
X + Y = 1
(14Y /3) + Y = 1
17Y = 3
Y = 3/17
X = 14/17

Therefore the steady state vector here is given as: (14/17, 3/17)

b) Let the steady state vector here be (X, Y, Z) here.

From second column, we have here:
Y = (4/5)X + (3/8)Y
(5/8)Y = (4/5)X
X = (25/32)Y

From third column, we have here:
Z = (3/7)Z
Z = 0

Also as X + Y + Z = 1
(25/32)Y + Y = 1
(57/32)Y = 1
Y = (32/57)
X = (25/57)

Therefore the steady state vector here is given as: (25/57, 32/57, 0)