Consider a random process $X(t) = Z(t)\sin(wt-Q)$. Here $Q$ is a random variable taking values $q$ in $[-\pi/2,\pi/2]$ with PDF given by
$$p_1^Q(q) = \frac{\cos(q)}{2}$$
$Z(t)$ is some random process which is statistically independent of $Q$
The question is "Express the mean value of $X(t)$ through the mean value of $Z(t)$"
I understand how to calculate the mean value of a random process defined by
$$E(t) = \int xp_1(x)~dx$$
So I've got $E[Z(t)] \int_{-\pi/2}^{\pi/2} 1/2\cos Q\sin(wt-Q)~dQ$
which after integrating I have $E[Z(t)]1/4\pi \sin(tw)$
assuming the integral calculation is correct, is this right? do I have to do any more with $Z(t)$?