The weather on any given day in a particular city can be sunny, cloudy, or rainy. it has been observed to be predictable largely on the basis of the weather on the previous day. specfically:

if it is sunny on one day, it will be sunny the next day 1/6 of the time, and be cloudy the next day 1/3 of the time

if it is cloudy on one day, it will be sunny the next day 1/6 of the time, and be cloudy the next day 1/6 of the time

if it is rainy on one day, it will be sunny the next day 1/2 of the time, and be cloudy the next day 1/6 of the time

using 'sunny', 'cloudy', and 'rainy' (in that order) as the states in a system, set up the transition matrix for a markov chain to describe this system.