Encik 'r'usuf is considering about investing in a Private Retirement Scheme (PR8). After studying various forms of investment, he has decided that only three providers suit his needs. These are Public Mutual Berhad, Kenanga Investors Berhad and AmFunds Management Berhad- The choice of PR8 providers depends on the interest rate since the return on the investment will be a function of this interest rate. Currently, the interest rate is considered quite volatile and can go up or down signicantly over the coming year. Based on the current return on investments, Encil-c Yusuf has developed the following table showing the payoffs of the investments after one year depending on the interest rate at the end of the year. Interest Alternative Public Mutual Kenanga Investors AmFunds Management Berhad PM Berhad KI Berhad AF RM 55 000 RM 35 000 RM so 000 High RM 100 000 RM 90 ODD RM 91 000 From his observation, the probability that the interest rate will be low is 0.55, and 0.45 that it will be high. He has a friend who claims to be able to forecast future market conditions. This service is available for a RM900 fee. The probability that the forecast is going to be favorable is 0.80. The following table shows the revised probabilities of past performance of the forecasting service. Given the survey The event that the actual interest rate is predicted the market Favorable 0.3 0.7 Unfavorable 0.6 0.4 Note: P(Low | Favourable) = 0.3 a) Construct a complete decision tree for this problem. (11 marks) b) Advise Encik 'r'usuf for the best decision. {2 marks) c) Compute the expected value of sample information. (2 marks}