Tutorial 3 - Discrete Random Variable Question 1 Suppose you make a RM1000 investment in a risky venture. There is a 40% chance that the payoff from the investment will be RM2000, a 50% chance that you will just get your money back, and a 10% chance that you will receive nothing at all from the investment. a) Find the expected value and standard deviation of the payoff from your investment of RM1,000. b) If X is the payoff from the investment, then the net profit from the investment is Y = X -1000. Find the expected value and standard deviation of the net profit. c) If you invest RM3000 in the risky venture instead of RM1000 and the possible payoffs triple accordingly, what is the expected value and standard deviation of the net profit from the RM3000 investment? Question 2 Suppose you work for an insurance company, and you sell a RM10,000 1-year term insurance policy at an annual premium of RM290. Actuarial tables show that the probability of death during the next year for a person of you customer's age, sex, health, etc is 0.001. What is the expected gain (amount of money made by the company) for a policy of this type? Question 3 An investor is given the following information about the returns on two stocks ( in percentage): Stock A B Mean 9 13 Standard Deviation 15 21 a) If she is most interested in maximizing he returns, which stock should she choose? b) If she is most interested to minimizing her risk, which stock should she choose? c) Compute the expected return and expected risk of the portfolio of 60% stock A and 40% stock B given that coefficient of correlation is 0.4. Question 4: Given the following probability distribution of X: x p(x) 0 0.25 1 0.40 2 0.20 3 0.15 (a) Find the mean and standard deviation of X. (b) Apply the laws of expected value and variance to find the following: E (3 X 2) ; E ( X 2) 2 ; Var (4 X ) 1