(Solved): The relationship between the random processes X(t) and Y(t), as Y(t) = X(t) tan ( t + )is given. ...

The relationship between the random processes X(t) and Y(t), as Y(t) = X(t) tan (ω t + θ)
is given. Here, X(t) is broadly a stationary process. θ and X(t) statistically independent. It varies uniformly between θ (-π , π).
a) Find the expected value of Y(t).
b) Determine the autocorrelation function of Y(t).
c) Determine whether Y(t) is ergodic.
d) Specify the spectral power density of Y(t) in terms of the spectral power density of X(t).