Let X(t) be a wide sense stationary random process with the power spectral density S_X(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response
H(f) =

As shown in figure (b). The output of the lowpass filter is Y(t)

Let E be the expectation operator and consider the following statements.
I. E(X(t)) = E(Y(t))
II. E((t)) = E((t))
III. E((t)) = 2
Select the correct option: