Find the steady state vector for this transition matrix

Question

        .6      .4

T=

         .55   .45 

Answer 1

Heather,

 

Drexel has a good webpage describing the calculations using matrix algebra at

https://www.math.drexel.edu/~jwd25/LM_SPRING_07/lectures/Markov.html

 

If its a little to technical, I'll summarize as needed for your problem

 

Given a transition matrix P (your transition matrix is rotated 90 degrees compared to those in the Drexel example), with

a , (1-a) 

(1-b), b

In your case a=.6 and b=.45

 

the steady state vector for a 2x2 transition matrix is a vertical matrix

(1-b)/[2-(a+b)] = .4/[2-(1.05)] = .4/.95   = 0.42105263157894736842105263157895

(1-a)/[2-(a+b)] = .55/[2-(1.05)] =.55/.95 = 0.57894736842105263157894736842105

 

You can round it to any degree of accuracy you care to, but note that these numbers add to 1.