Suppose that you have $5000 and you are contemplating the purchase of two investments, IBM and Walgreen's. One year from now, IBM can be sold at $ X per dollar invested, and Walgreen's can be sold for $ Y per dollar invested. You regard X and Y to be statistically independent Normal random variables with expected value 1.1 and variance 0.04.
(a) If you put all your money in IBM, what is the probability that you will be able to sell it one year from now at a positive profit?
(b) If you split your money evenly between the two investments, what is the probability you will be able to sell your portfolio a year from now at a positive profit?