every morning aaron is equallly likely to bring his laptop o

every morning, aaron is equallly likely to bring his laptop or mp3 player to his office. if there is only only of this at home he pucks it up with probability 1. At night, he leaves office and forgets each itme independeltly with 0.5 probability. If he brought only his mp3 player in the morning, he forgets it in the office 100% of the time.

1-determine states of this markov chain and construct the probability transition matrix.

2-what is the fraction of time he forgets his laptop in the office.

3-what is the average duration of time his mp3 player stays at the office?

4-if both his laptop and mp3 player are innitially at home, how many days on the average does he have nothing left in the office untill he forgets both?

Solution

2)

0.5

3) 0.5 * 1 = 0.5

4)

0.5 * 1 + 1 * 0.5 = 1