Total Marks: 10 Suppose that the weather can only be sunny or raining, and that the weather conditions on successive mornings form a Markov chain with stationary transition probabilities. Suppose that the transition matrix is as follows: Sunny Raining Sunny Raining 0.7 0.3 0.4 0.6 ! (a) If it rains on Friday, what is the probability that it is sunny on Saturday and Sunday? (2 marks) (b) If it is sunny on Monday, what is the probability that it will be sunny on Wednesday? (2 marks) (c) If it is sunny on Monday and Wednesday, what is the probability that it is sunny on Tuesday?