Statistics II - Old Questions

9. In some town, each day is either sunny or rainy. A sunny day is followed by another sunny day with probability 0.7, whereas a rainy day is followed by a sunny day with probability 0.4. Weather conditions in this problem represent a homogeneous Markov chain with 2 states: state 1 = “sunny” and state 2 = “rainy.” Transition probability matrix of sunny and rainy days is given below.

Compute the probability of sunny days and rainy days using the steady-state equation for this Markov chain.