Problem 2 We consider the weather in Vancouver in winter to be either cloudy (C), snowy (S) or rainy (R). The weather stays cloudy for an exponential time duration of parameter 1 per day, before it either rains with probability 0.9, or snows with probability 0.1. The time for the rain and snow to stop (so the weather gets cloudy) is exponential with parameters 2 per day and 4 per day, respectively. a. Describe this situation using a continuous-time Markov chain and give the parameters of the model in terms of qij, with i,j being either R, C or S. b. Write the Backwards and Forwards Kolmogorov equations associated with Pc,c(t) c. In the long run, what is the proportion of time when it is snowing?