c. For each day the state of the weather can be either dry or rainy. If today is dry, the probability that it will be dry tomorrow is 0.70, and the probability that it will be rainy tomorrow is 0.30. Conversely, if today is rainy, the probability that tomorrow will be dry is 0.20, and the probability that tomorrow will be rainy is 0.80. Let P be a vector containing the probabilities that it is dry or rainy today, such that _ Pd P (a) 0'50). How is P updated for tomorrow? Can you work out a 2X2 matrix 0.50 that allows P to be updated from day to day? (Hint: the matrix contains the four probabilities above that It is known for today that P = ( allow P to be calculated for the following day]