Covariance of spouses' incomes from correlation

Question

Among couples, the husband's annual income has mean $60k and standard deviation $13k, and the wife's has mean $55k and standard deviation $11k. The two incomes have correlation $0.85$ . Find their covariance in (thousands of dollars) $^2$ .

Short answer

$121.55$ . Covariance is correlation times the two standard deviations: $0.85\times13\times11=121.55$ . The means are irrelevant.

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Lessons behind this question

Maximum Likelihood Estimation: Score and Log-Likelihood
Covariance and Correlation
Populations, Samples, and Sampling Distributions

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