Prove that $\displaystyle E[\bold{F}(j \omega_{1})\bold{F}^{*}(j \omega_{2})) = 0 $ for $\displaystyle \omega_1 \neq \omega_2 $ where $\displaystyle \bold{F}(j \omega) $ is the Fourier transform of a stationary random process, $\displaystyle \bold{x}(t) $ as $\displaystyle F(j \omega) = \int_{-\infty}^{\infty} x(t)e^{-j \omega t} \ dt $.


So if $\displaystyle \omega_1 = \omega_2 $ then the expected value is zero.