I was able to solve the transition matrix and state vector and I know how to figure out the probability for 2 weeks if it was high, but I can't figure out that last part.
If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. If volume is low this week then it will be high next week with a probability of 0.3. The manager estimates that the volume is five times as likely to be high as to be low this week. Assume that state 1 is high volume and that state 2 is low volume.
Transition matrix P for this Markov chain: P=[.6 .4
.3 .7]
State vector that represents the manager's estimate X=[5/6 1/6]
Suppose, contrary to the manager's estimate, that this week the volume is low. How many weeks must pass before a week comes along in which the probability of high volume is at least 0.3?
If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. If volume is low this week then it will be high next week with a probability of 0.3. The manager estimates that the volume is five times as likely to be high as to be low this week. Assume that state 1 is high volume and that state 2 is low volume.
Transition matrix P for this Markov chain: P=[.6 .4
.3 .7]
State vector that represents the manager's estimate X=[5/6 1/6]
Suppose, contrary to the manager's estimate, that this week the volume is low. How many weeks must pass before a week comes along in which the probability of high volume is at least 0.3?