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# Just need some clarification

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If i have the transition matrix:

$$\begin{pmatrix} 0.72 & 0.15 & 0.16 \\ 0.14 & 0.72 & 0.12 \\ 0.14 & 0.13 & 0.72 \end{pmatrix}$$

Where the first column represents ST, second being ACM and third being OR.

If I want to find the probability of getting ACM for two time periods would i multiply the transition matrix by the following to the power of 2?

$$\begin{pmatrix} 0\\ 1\\ 0 \end{pmatrix}$$

May 31, 2020

#1
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I'm not sure I've interpreted your question correctly, but, if I have, then the following should be relevant.

I've assumed you start in state ACM, in which case the probability that you are back in ACM after two transition periods is 0.555.

The probabilty that you stay in ACM for two consecutive periods is just 0.72^2.

However, there is a significant probability that I've totally misinterpreted your question!!

May 31, 2020
edited by Alan  May 31, 2020
edited by Alan  May 31, 2020
edited by Alan  May 31, 2020
#2
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Thnkyou Alan that is awesome! Very detailed, muchly appreciated

lhyla02  Jun 1, 2020