A Mutual fund investor has choice of stock fund (Fund 1), a bond fund (Fund 2) and money market fund (Fund 3). At the end of each quarter he can move his money from fund to fund. The probability he stays in Fund 1 is 0.60, in Fund 2 is 0.50 and in Fund 3 is 0.40. If he switches funds, he will move to each of the other funds with equal probability. Assume he starts with all his money in Fund 1.
(A) Determine the transition matrix and the two step transition matrix?
(B) Find the fixed point vector for this Markov Chain?