Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal lowpass filter with the frequency response:\(H\left( f \right) = \left\{ {\begin{array}{*{20}{c}} {1,}&{\left| f \right| \le \frac{1}{2}Hz}\\ {0,}&{\left| f \right| > \frac{1}{2}Hz} \end{array}} \right.\)This is as shown in Figure (b). The output of the lowpass filter is Y(t).Let E be the expectation operator. Consider the following statements:I. E(X(t)) = E(Y(t))II. E(X2(t)) = E(Y2(t))III. E(Y2(t)) = 2Select the correct option:

Let X(t) be a wide sense stationary random process with the power spec

1.	Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal lowpass filter with the frequency response:\(H\left( f \right) = \left\{ {\begin{array}{*{20}{c}} {1,}&{\left\| f \right\| \le \frac{1}{2}Hz}\\ {0,}&{\left\| f \right\| > \frac{1}{2}Hz} \end{array}} \right.\)This is as shown in Figure (b). The output of the lowpass filter is Y(t).Let E be the expectation operator. Consider the following statements:I. E(X(t)) = E(Y(t))II. E(X2(t)) = E(Y2(t))III. E(Y2(t)) = 2Select the correct option:
A.	only I is true
B.	only II and III are true
C.	only I and II are true
D.	only I and III are true
Answer» B. only II and III are true