Problem 1. (6pts) We use the following 1st order Markov chain to model the weather. The transition probabilities are dened as follows: 0 Pr(t0morrow is sunny I today is sunny) : 0.8 o Pr(t0morrow is rainy | today is sunny) : 0.2 o Pr(t0n10rr0w is sunny | today is rainy) : 0.5 o Pr(t0morrow is rainy | today is rainy) : 0.5 In the long term, What's the probability of rainy weather tomorrow? (Hint: Consider the stationary distribution of the Markov Chain)