An investor has $1,000 to invest and two investment opportunities, each requiring a minimum of $500. The profit per $100 from the first can be represented by a random variable X, having the following probability distributions:

P1X = -52 = 0.4 and P1X = 202 = 0.6 The profit per $100 from the second is given by the random variable Y, whose probability distributions are as follows:

P1Y = 02 = 0.6 and P1Y = 252 = 0.4 Random variables X and Y are independent. The investor has the following possible strategies:

a. $1,000 in the first investment

b. $1,000 in the second investment

c. $500 in each investment Find the mean and variance of the profit from each strategy.