What is the covariance between the random variable Y and itself, Cov(Y, Y)? What

Question

What is the covariance between the random variable Y and itself, Cov(Y, Y)? What is the correlation between a random variable and itself? Choose the correct answer below.

A. The covariance between Y and itself is the expected value of the mean. The correlation between Y and itself is the variance of Y divided by the covariance between Y and itself.

B. The covariance between Y and itself is the correlation between Y and itself. The correlation between Y and itself is the covariance between Y and itself.

C. The covariance between Y and itself is the variance of Y. The correlation between Y and itself is 1.

D. The covariance between Y and itself is the standard deviation of Y. The correlation between Y and itself is the variance of Y.

Explanation / Answer

The answer is C. When you talk about covariance, you are dealing with two different variables and therefore the covariance of a variable itself is actually variance. Also, correlation between y and itself will be 1 because y is totally related to itself

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