State Vectors: Markov chain, high and low volumes

Angela123

Junior Member
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Oct 9, 2008
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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?
 
The manager's estimate shouldn't matter since it is not the actual state. The current state vector is \(\displaystyle p_0 = \[\begin{pmatrix} 0 & 1 \end{pmatrix}\]\). Find \(\displaystyle p_1 = p_0 P\) and see what you get.
 
I have to use the manager's estimate. That's how I'm supposed to do it on the homework.
 
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