Q$2.$ In mobile communications systems, Doppler shift may occur, causing random frequency shift of the carrier. The presence of noise causes random variation of the amplitude of the carrier. In such cases, the received signal can be modeled by a random process $x(t).$ Consider one of these systems, with is $x(t)=cos(2Ft),$ where $F$ is a uniform random variable in the range $0,f_0.$ Calculate the following:

The ensemble average of $x(t)$

The ACF of $x(t)$

The time average of $x(t)$

The time ACF of $x(t)$