Adelaide weather Markov chain example
Channel: David Roberts
Date: 2014-06-18

This example, from pages 96/98 in the notes and reproduced below, treats a Markov chain as defined in class, now with three states. I find the long-term behaviour of the system in terms of the unique steady-state vector for the matrix.

==== Problem description ====
Suppose that there are three states for the local weather: sunny, cloudy and raining. If today is sunny, the probability tomorrow is sunny is 0.7, cloudy 0.2 and raining 0.1; while if today is cloudy the probability tomorrow is sunny is 0.5, cloudy 0.3 and raining 0.2; and if today it is raining then tomorrow will be sunny with a probability of 0.2, cloudy with a probability of 0.5 and still raining with a probability of 0.3.