Let m= the number of Mercedes E550s delivered to the dealership at one time (both initially and subsequently), and let p= the probability an E550 is sold in any particular week (m = 5 and p = .3 in the previous exercise). Determine the steady-state probabilities for this chain and then the average number of weeks between vehicle orders.
> D
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.0 0.0 0.0 0.0 0.0 1.0
[2,] 0.3 0.7 0.0 0.0 0.0 0.0
[3,] 0.0 0.3 0.7 0.0 0.0 0.0
[4,] 0.0 0.0 0.3 0.7 0.0 0.0
[5,] 0.0 0.0 0.0 0.3 0.7 0.0
[6,] 0.0 0.0 0.0 0.0 0.3 0.7
I know I have the transition matrix right for m = 5 and p = 0.3, but I'm stuck on how to create the transition matrix and find the steady state probabilities using just variables
Just multiply the matrix with itself until all columns converge to the same vector, that's the steady state