Which of the following is the formula for the covariance between X and Y?
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A. B. C. D.B
E[(X - E(X))*(Y - E(Y))] is the covariance between X and Y.
The formula for the covariance between two random variables X and Y is given by:
Cov(X, Y) = E[(X - E(X))(Y - E(Y))],
where Cov(X, Y) represents the covariance between X and Y, E(X) represents the expected value (or mean) of X, E(Y) represents the expected value (or mean) of Y, and E[.] represents the expectation operator.
Let's go through the answer choices to determine which one represents the correct formula for covariance:
A. (X - E(X))*(Y - E(Y)): This answer choice does not include the expectation operator, so it does not calculate the covariance correctly. It only calculates the product of the differences between X and its mean, and Y and its mean.
B. E[(X - E(X))*(Y - E(Y))]: This answer choice is correct. It includes the expectation operator E[.] and calculates the product of the differences between X and its mean, and Y and its mean. Taking the expectation of this expression gives us the covariance between X and Y.
C. E[(X + E(X))*(Y + E(Y))]: This answer choice is incorrect. It includes the expectation operator but uses addition instead of subtraction. The correct formula for covariance involves subtracting the means, not adding them.
D. E[XY - E(XY)]: This answer choice is incorrect. It represents the formula for the covariance between XY and E(XY), not X and Y. It does not calculate the covariance between X and Y accurately.
Therefore, the correct answer is B. E[(X - E(X))*(Y - E(Y))], which represents the formula for the covariance between X and Y.