Question

Whenever a commuter has travelled by car, then the next day there is probability 1/3 that he takes the car and probability 2/3 that he takes the train. Whenever he has travelled by train, then the next day there is probability 1/2 that he takes the car and probability 1/2 that he trakes the train.

Write out the transition matrix for this Markov chain.

Help is greatly appreciated!

Answer 1

I'm not very familiar with Markov chains, but I would think it is just \(\left(\begin{smallmatrix}1/3&1/2\\2/3&1/2\end{smallmatrix}\right)\)

Answer 2

I'm too stupid to figure out how to make a 2x2 matrix, so you'll have to deal with this:
\[T = \left[ \frac{1}{3} \ \frac{2}{3} || \frac{1}{2} \ \frac{1}{2} \right]\]
Assume [1/3 2/3] (car and train probability)
...
Well anyway, you should be able to follow this guide:
https://docs.google.com/viewer?url=http%3A%2F%2Fwww.math.ncsu.edu%2Fma114%2FPDF%2F6.3.pdf

Answer 3

ICantnameme, is the 1/3 at the top and then the 2/3 underneath or beside it?

Answer 4

1/3 and 2/3 on the top row, 1/2 and 1/2 on the bottom row like the person at top posted. I couldn't figure out how to do it.