Variable x is a controllable, and variable y is a random varialbe. Also, y=b*x+u, and u is a random iterm. So x and y is correlated. But, if we calculate the covariance between x and y, according to the definition Cov(x,y)=E[(x-Ex)(y-Ey)], the value should be zero. Since Ex=x.
Is the conclusion correct?Thanks