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Let X and Y be two random variables with covariance Cov(X,Y) = 3 and variances Var(X) = 4 and Var(Y) = 9. What is the correlation coefficient between X and Y?Review Later1/31/21/41/5

Question

Let X and Y be two random variables with covariance Cov(X,Y) = 3 and variances Var(X) = 4 and Var(Y) = 9. What is the correlation coefficient between X and Y?Review Later1/31/21/41/5

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Solution

The correlation coefficient (ρ) between two random variables X and Y can be calculated using the formula:

ρ(X,Y) = Cov(X,Y) / sqrt[Var(X) * Var(Y)]

Given that Cov(X,Y) = 3, Var(X) = 4, and Var(Y) = 9, we can substitute these values into the formula:

ρ(X,Y) = 3 / sqrt[4 * 9] = 3 / sqrt[36] = 3 / 6 = 0.5

So, the correlation coefficient between X and Y is 0.5.

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