Final answer:
The statement is true: the expectation of the product of two random variables is the same as their covariance when at least one of the two random variables has a zero mean.
Step-by-step explanation:
The statement that the expectation of the product of two random variables is the same as their covariance when at least one of the two random variables has a zero mean is true.
To see why this is true, let's consider two random variables X and Y with a covariance of Cov(X, Y) and an expectation of E(XY), and assume that X has a zero mean. The covariance between X and Y can be calculated as Cov(X, Y) = E((X - E(X))(Y - E(Y))). Since X has a zero mean, we have Cov(X, Y) = E(XY - E(X)Y) = E(XY) - E(E(X)Y) = E(XY) - E(X)E(Y) = E(XY).
This shows that the expectation of the product of X and Y is indeed the same as their covariance when X has a zero mean.