Determine whether the stochastic matrix P is regular. Then find the steady state matrix X of the Markov chain with matrix of transition probabilities P. P= 0.22 0.20 0.65
0.62 0.60 0.15
0.16 0.20 0.20

Step-by-step explanation:

Given that:

For a steady-state of a given matrix

As a result P = and a+b+c must be equal to 1

So, if P =

Then;

Equating both equation (1) and (3)

(0.22a+ 0.2b + 0.65c) - (0.16a + 0.2b + 0.2c) = a - c

0.06a + 0.45c = a - c

collect like terms

0.06a - a = -c - 0.45c

-0.94 a = -1.45 c

0.94 a = 1.45 c

Using equation (2)

0.62a + 0.60b + 0.15c = b

where;

c = 94/145 a

From a + b + c = 1

∴

∴

The steady matrix of is:

the correct answer is $7.38

step-by-step explanation:

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