An investor puts some money into each of two stocks labeled A and B: $500 in to stock A and $1000 in to stock B. The mean rates of return for the stocks are: Stock A = 0.15 and Stock B = 0.12. So, if one puts a dollar into stock A, the expected profit at the end of the year is $0.15. The standard deviations of the rates of returns are: Stock A = 0.05 and Stock B = 0.03.

a) Find the mean and standard deviation of the total amount the investor earns in one year, assuming the rates of return are independent random variables.

b) Find the mean and standard deviation of the total amount the investor makes in one year, assuming that the rates of return are positively correlated with a correlation coefficient of 0.5.