Let the stationary random process X(t) be bandlimited to [−ω c ,+ω c ] where ωc is a positive real number. Then define Y (t) as the output of an ideal lowpass filter with passband [−ω 1 ,+ω 1 ] and input random process X(t). (1) Show that X(t) = Y (t) in the m.s. sense if ω 1 > ω c . (2) In the above case, also show that X(t) = Y (t) with probability-1.