Answer needed

a) A study has determined that the occupation of a boy as an adult, depends upon the occupation of his father and is given by the following transition matrix, where P = professional, F = farmer, and L = laborer Father's occupation P F L P 0.8 0.3 0.2 Son's occupation F 0.1 0.5 0.2 L 0.1 0.2 0.6 Thus the probability that son of a professional will also be a professional is 0.8 and so on. i) What is probability that the grandchild of a professional will be a farmer? ii) In the long run, what proportions of the population will be former? b). Suppose that the weather in a certain city is either rainy or dry. As a result of extensive record keeping it has been determined that the probability of a rainy day following a dry day is = , and the probability of a rainy day following a rainy day is - . Let state D be a dry day and state R be a rainy. Suppose that when we begin our observation (0 day), it is dry (i) What is the initial state vector for the Markov process? (ii) What is the transition matrix for the Markov process? (iii) State whether the Markov process reaches the equilibrium