Examples of Markov Chains - A Very Simple Weather Model

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:

 P = \begin{bmatrix} 0.9 & 0.1 \\ 0.5 & 0.5 \end{bmatrix}

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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