It is known that in the legendary frozen town of Kholod the weather displays the following patterns:
- If it snows on one day then there is a probability of 0.8 that it will snow on the following day
- If it does not snow on one day then there is a probability of 0.6 that it will also not snow on the following day
Represent this information as
(i) a transition state diagram
(ii) a transition matrix.
Let be the transition matrix found in part (a)(ii).
By first finding an appropriate power of the matrix , find the probability that it will snow on Friday, given that it did not snow on the preceding Tuesday.
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