Question: His and her earnings Researchers randomly select a married couple in which both spouses are employed. Let X be the income of the husband and Y be the income of the wife. Suppose that you know the means mX and mY and the variances s2X and σ2Y of both variables.
(a) Is it reasonable to take the mean of the total income X + Y to be μX + μY? Explain your answer.
(b) Is it reasonable to take the variance of the total income to be σ2X + σ 2Y? Explain your answer.