Can you help me with this Markov chain problem? This should be simple, but my brain is not working well.
Let $\{{x_t}\}_{t=0}^\infty$ follows a Markov chain. Each $x_t$ can take two values: {G,B} (good or bad. bad represents a disaster). The transition probabilities are two unknowns:
Pr(G | G) = x
Pr(G | B) = y
You know the following:
-$x_0 = G$
-Expected duration of a disaster is d periods.
-The average frequency of disasters is f disasters per 100 periods
What are x and y?
Thank you.