The risk-free rate (per annum with semi-annual compounding) is 5%. You have a portfolio worth 10000 dollars today. Let X be the return of your portfolio in 6 months. (The return means the gain, or increase, if positive, in your portfolio value. If the return is negative it means your portfolio value decreased.) Suppose the p.d.f. of X is given by

fX(x) = (x + 50)/ 80000 if 50 x 350, and 0 otherwise

(a) Compute the expected rate of return. (b) What is the probability that your portfolio will lose money in 6 months? (c) Are you risk-neutral, risk-averse, or risk-prone? Justify your answer.