Given $X(t)=A\cos(2\pi ft+\phi )$ where A and $\phi$ are independent. f and t are constant
(1) For $A\sim a(\operatorname{constant})$ what is the expected value $E[X(t)]$ and Autocorrelation $R_X$? Is it Wide Wense Stationary?
(2) For $A\sim \operatorname{Uniform}(0,2)$; $\phi=\operatorname{Uniform}(0, \pi/2)$ what is the expected value $E[X(t)]$ and Autocorrelation $R_X$? Is it Wide Sense Stationary?
(3) For $A\sim \operatorname{Uniform}(0,2)$; $\phi=\operatorname{Uniform}(-\pi, \pi)$ what is the expected value E[X(t)] and Autocorrelation $R_X$? Is it Wide sense Stationary?
(4)For $A\sim a(\operatorname{constant})$ .Now given at $\phi=0$,X(t)=1/2 and at $\phi=\pi/2$,X(t)=1/2. what is the expected value?
Answers I got
1)I got $0$ and $A\cos(2\pi f\tau)$. It is WSS (I want to confirm this answer).
2)$A/(2\pi)$ and not getting autocorrelation. However I was not able to make out if this is WSS. Any help appreciated.
3)$0$ and an expression. It is WSS(I want to confirm this answer)
4)I got the expected value as $\pi/4$.(No correlation was asked). It is WSS(I also want to confirm this answer)