Recovering a covariance from a known correlation

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Two quantities have correlation 0.5. One has variance 36 and the other has variance 64. What is the covariance between them?

Accepted Answer

The correlation is the covariance divided by the two standard deviations, so to go the other way we simply multiply back: \mathrm{Cov}(X, Y) = ho \cdot \mathrm{SD}(X)\,\mathrm{SD}(Y). In words: rebuild the covariance by putting the units back, multiplying the correlation by both standard deviations. Get the standard deviations. \mathrm{SD}(X) = \sqrt{36} = 6, \qquad \mathrm{SD}(Y) = \sqrt{64} = 8. Multiply. \mathrm{Cov}(X, Y) = 0.5 	imes 6 	imes 8 = 24. Takeaway. Correlation and covariance are two views of the same link: divide by the spreads to get correlation, multiply them back to get …

Recovering a covariance from a known correlation

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