Suppose whether it rains or now depends on previous weather conditions through the last two days: it will rain tomorrow with probability 0.7 if it has rained in the past two days; 0.5 if it rained today but not yesterday; 0.4 if it rained yesterday but not today; 0.2 if it hasnt rained in the past two days. Construct a DTMC with a properly de ned state space, and use it to compute the long-run proportion (probability) of rainy days.