Problem I am working on is as follows ;
Suppose that whenever the Washington Wizards win a game, they will also win the next one with probability 0.75 and lose it with probability 0.25. However, if the team loses a game, then they win the next one with probability 0.40 and lose it with probability 0.60. The consecutive results obtained by the team is a Markov chain.
One of the questions asks the following;
If the team is scheduled to play 82 games during the season, what is the expected overall record of wins vs. losses?
What I have done so far?
1) Created the transition matrix (State 0: Losing the match, State 1: winning the match) $$ T = \begin{bmatrix} 0.60 & 0.4\\ 0.25 & 0.75\\ \end{bmatrix} $$
2) Found the steady-state probabilities using steady-state equations ;
$$ \pi_0\ = 5/13 $$ $$ \pi_1\ = 8/13 $$
3) Assumed that team will earn 1 point if it wins a game (and 0 if it loses) and for a single game
$$\sum_{i=0}^1 c(i)*\pi_i\ = (1)*8/13 + (0)*5/13 = 8/13 $$
So does it make sense to multiply this result with 82, to come up with 82 games' expected overall record of wins vs losses?
Thanks
