If two random variables X and Y are statistically independent,then Cov(X,Y)= 0.

Question

Quizplus · Accepted Answer

If X and Y are statistically independent, it means that the occurrence or value of one variable does not affect the occurrence or value of the other variable. Mathematically, this is represented by E(XY) = E(X)E(Y), where E denotes expectation. Using this equation and the formula for covariance, Cov(X,Y) = E(XY) - E(X)E(Y), we can see that Cov(X,Y) = 0 when X and Y are independent.

If Two Random Variables X and Y Are Statistically Independent,then