Markov Transition Matrix for the Sequence $W W L L L L W L W L L$

Question

I am trying to determine the Markov Transition Matrix for the sequence in the following statement:

A team in the first 11 games of a championship match has the secuence: $W W L L L L W L W L L$ where $W$ represents a win and $L$ represents a loss.

The only thing I understand properly is that the sum of each row must add up to $1$.

What I've Tried:

I tried creating a 2 x 11 matrix where the rows will be a win and a loss and the columns will be for each game but I was told that was incorrect.

How do I go about constructing the Markov Transition Matrix for the above sequence?

Answer 1

I don't know what exactly is meant by the transition matrix for a finite sequence, but maybe it's this:

One of the four W is followed by a W, while three out of four are followed by L;
two of the six L are followed by W, while four out of six are followed by L (there's a seventh L, but it isn't followed by anything);
so the matrix is $$\pmatrix{1/4&3/4\cr1/3&2/3\cr}$$

Answer 2

A Markov process is defined by transition probabilities between states. In the best case, here you have a finite sample from which you can estimate probabilities.