A Very Simple Weather Model
The probabilities of weather conditions (modeled as either rainy or sunny), given the weather on the preceding day, can be represented by a transition matrix:
The matrix P represents the weather model in which a sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. The columns can be labelled "sunny" and "rainy", and the rows can be labelled in the same order.
(P)i j is the probability that, if a given day is of type i, it will be followed by a day of type j.
Notice that the rows of P sum to 1: this is because P is a stochastic matrix.
Read more about this topic: Examples Of Markov Chains
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