# Thread: Markov Chain & Transition Probability Matrix

1. ## Markov Chain & Transition Probability Matrix

Hi there, I have a question here which I still couldn't figure it out. Can anyone here help me with it? Thanks.

Five balls are distributed between 2 urns A and B. Each period, an urn is selected at random, and if it is not empty, a ball from that urn is removed and placed into the other urn.

Let Xn denote the number of balls in the urn A.
a) Write down the transition matrix of this chain.

2. ## Re: Markov Chain & Transition Probability Matrix

Assuming if there are 0 balls in one urn, and that urn is chosen, you pick a ball from the other urn and put into the empty urn.

$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 & 0 \\ 0.5 & 0 & 0.5 & 0 & 0 & 0 \\ 0 & 0.5 & 0 & 0.5 & 0 & 0 \\ 0 & 0 & 0.5 & 0 & 0.5 & 0 \\ 0 & 0 & 0 & 0.5 & 0 & 0.5 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0\end{pmatrix}$

3. ## Re: Markov Chain & Transition Probability Matrix

Thanks.. hehhee..