Bob is taking a stoehastic process class and each week, his performance could be
ID: 3244330 • Letter: B
Question
Bob is taking a stoehastic process class and each week, his performance could be above average, average, or behind for each week. If he is above average in one week, he will be average or behind in the next week with probability 0.3 or 0.2 respectively. If he is average in one week, he will be above average or behind in the next week with probability 0.3 or 0.3 respectively. If he is behind in one week, he will be above average or average in the next week with probability 0.1 and 0.6 respectively. To model the problem, we set state 1 to be "above average", state 2 to be "average", and state 3 to be "behind". The transition matrix is given as below P = (0.3 0.2 0.3 0.4 0.3 0.1 0.6 0.3) The two-step and three-step transition matrices are given as below If Bob is equally likely to be above average, average, and behind at week 0, what's the probability that he will be above average at week 2?Explanation / Answer
here given that state 1 represents that " Above average"
state 2 represents that " Average"
state 3 represents that " Behind"
And we have given TPM matrix ( P ) for 1st week
TPM matrix (P^2) for 2nd week
TPM matrix (P^3) for 3rd week
Therefore the probability that Bob will be above average at 2nd week = P^2(1, 1) = 0.36