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


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