Let X(t) = A(t) sin(ωt + Φ), where A(t) and Φ are independent, nonnegative random variables for all t, and let Φ be uniformly distributed over [0, 2π]. Verify: If {A(t), t ∈ (−∞, +∞)} is a weakly...

Let X(t) = A(t) sin(ωt + Φ), where A(t) and Φ are independent, nonnegative random variables for all t, and let Φ be uniformly distributed over [0, 2π].

Verify: If {A(t), t ∈ (−∞, +∞)} is a weakly stationary process, then the stochastic process {X(t), t ∈ (−∞, +∞)} is also weakly stationary.