(Solved): The weather on any given day in a particular city can be sunny cloudy or rainy. It has been observe ...

The weather on any given day in a particular city can be sunny cloudy or rainy. It has been observed to be predictable largely or the basis of the weather on the previous day. Specfically - If it is sunny on one day, it will be sunny the next day \( 1 / 2 \) of the time, and be cloudy the next day \( 1 / 2 \) of the time - If it is cloudy 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 - If it is rainy on one day it will be sunny the next day \( 1 / 3 \) of the time, and be cloudy the next day \( 1 / 3 \) 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 Use your matrix to determine the probability that it will rain on Thursday if it is sunny on Sunday \[ P=\left[\begin{array}{lll} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right] \] Probability of rain on Thursday \( =0 \)