Markov Chain Limiting Probabilities (Just need answer checked please)

• Aug 9th 2011, 09:36 PM
downthesun01
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

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

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

I just wanna make sure this is correct, and if not, what I'm doing wrong. Thanks
• Aug 9th 2011, 11:04 PM
CaptainBlack
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

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

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

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
• Aug 10th 2011, 12:24 AM
downthesun01
Re: Markov Chain Limiting Probabilities (Just need answer checked please)
Thank you very much