A class of modulated random signals Y(t) is defined by Y(t) = AX(t)cos( c t + )

A class of modulated random signals Y(t) is defined by 

Y(t) = AX(t)cos(ω _c t + ϕ) 

where X(t) is the random message and Acos(ω _c t + ϕ) is the carrier. The random message signal X(t) is a zero-mean stationary random process with autocorrelation RX(τ). The carrier amplitude A and the carrier frequency ω _c are constants, and the phase ϕ is a uniform random variable over (0,π). Assuming that X(t) and ϕ are independent, find: 

(a) the mean of y(t). 

(b) the autocorrelation of y(t). 

(c) Determine whether y(t) is WSS.