If [math]X[/math] and [math]Y[/math] are any two random variables, then the covariance of [math]X[/math] and [math]Y[/math] is defined by [math]\rm Cov(X,Y) = E((X - E(X))(Y -E(Y)))[/math]. Note that [math]\rm Cov(X,X) = V(X)[/math]. Show that, if [math]X[/math] and [math]Y[/math] are independent, then [math]\rm Cov(X,Y) = 0[/math]; and show, by an example, that we can have [math]\rm Cov(X,Y) = 0[/math] and [math]X[/math] and [math]Y[/math] not independent.