I have two random process: $$A(at)$$ $$\cos(2\pi f_0t+\Phi)$$ with these hypothesis:

1. $a$ and $f_0$ are constant
2. $\Phi$ is uniformly distributed in $[0,\pi)$
3. $A(at)$ is WSS

I must calculate the statistical averages and autocorrelation of the random process: $$X(t)=A(at)\cos(2\pi f_0t+\Phi)$$ I started to define the integral $$E[X(t)]=\frac{1}{\pi}\int_0^\pi A(at)\cos(2\pi f_0t+\phi)d\phi$$ but I think is wrong because i don't know how to consider the process $A(at)$