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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 s²_X and σ²_Y of both variables.

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

(b) Is it reasonable to take the variance of the total income to be σ²_X + σ²_Y? Explain your answer.

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