Redo exercise 14 in section 8.2 of your textbook, about the volume of securities sold by a brokerage firm, using the following data:
(i) if volume is high this week, then next week it will be high with probability of 0.9 and low with a probability of 0.1.
(ii) if volume is low this week then it will be high next week with a probability of 0.5
Assume that state 1 is high volume and that state 2 is low volume
1. find the transition matrix of this Markov process
P=
2. find the four-step transition matrix P(4)
P(4)=
3. if the volume is high this week, what is the probability that it will be high 4 weeks from now (use P(4))
4. if the volume is high this week, what is the probability that it will be low 4 weeks from now (use your answer to the preceding question to derive the answer to this question if you can)