(1) If volume is high this week, then next week it will be high with a 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. (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) Find the transition matrix for 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)?

Consider the statement from the equation as shown below: Here, (I) If volume is high this week, then next week it will be high with a 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 a probability of 0.5.(1) Assume, state 1 is high volume and state 2 is low volume, then the transition matrix for this Markova process is Hence, that’s the transition matrix. (2) Here, the N-step transition matrix p is pN then the four-step transition matrix p4 Hence, that’s the four-step transition matrix.