3. An investor will organize a forum to exhibit an education product on the coming Sunday. The success of the event depends on the weather condition on that day which could be one of the following three possibilities: Good (G), Moderate (M) and Raining (R). The returns and probabilities together with a risk-free opportunity (e.g. deposit money in a bank) are given below Outcomes Total Returns Probability G 5.00 0.4 M 1.25 0.4 R -0.25 0.2 Risk-free 1.50 1.0 The investor's utility function is U(x) = ln(x - K), where 0.750 with probability 0.4, if weather is Good, K = 0.625 with probability 0.4, if weather is Moderate, 0.500 with probability 0.2, if weather is Raining. How to invest in the risky asset and the risk-free one? What is the value of E[U(r)] according to the optimal portfolio? [15 marks)