A study of working couples measures the income X of the husband and the income Y of the wife in a large number of couples in which both partners are employed. Suppose that you knew the means X and Y and the variances X2 and Y2 of both variables in the population.

(a) Is it reasonable to take the mean of the total income X + Y to be X + Y? Explain your answer.

(b) Is it reasonable to take the variance of the total income to be X2 and Y2? Explain your answer.