Markov Chain Limiting Probabilities (Just need answer checked please)

*Three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck . What fraction of vehicles on the road are trucks?*

Let

state 0 represent seeing a truck

state 1 represent seeing a car

Then we have a probability matrix of

http://i54.photobucket.com/albums/g1...1/matrix-3.png

$\displaystyle \pi_{0}=0.25\pi_{0}+0.2(1-\pi_{0})$

$\displaystyle 0.95\pi_{0}=0.2 =>\pi_{0}=\frac{2}{95}$

I just wanna make sure this is correct, and if not, what I'm doing wrong. Thanks

Re: Markov Chain Limiting Probabilities (Just need answer checked please)

Quote:

Originally Posted by

**downthesun01** *Three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck . What fraction of vehicles on the road are trucks?*
Let

state 0 represent seeing a truck

state 1 represent seeing a car

Then we have a probability matrix of

http://i54.photobucket.com/albums/g1...1/matrix-3.png
$\displaystyle \pi_{0}=0.25\pi_{0}+0.2(1-\pi_{0})$

$\displaystyle 0.95\pi_{0}=0.2 =>\pi_{0}=\frac{2}{95}$

I just wanna make sure this is correct, and if not, what I'm doing wrong. Thanks

Up until the very last step, the answer is 0.2/0.95=20/95 ~= 0.2105

CB

Re: Markov Chain Limiting Probabilities (Just need answer checked please)