Let X (t) be a wide sense stationary Gaussian random process and form a new process according to Y (t) X (t) cos (t ) where and are constants and is a random variable uniformly distributed over 0, 2x and independent of X (t) (a) Is Y (t) wide sense stationary (b) Is Y (t) a Gaussian random process ...

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Let X (t) be a wide sense stationary Gaussian random process and form a new process according

Question:

Let X (t) be a wide sense stationary Gaussian random process and form a new process according to Y (t) = X (t) cos (ωt + θ) where ω and θ are constants and is a random variable uniformly distributed over [0, 2x] and independent of X (t).
(a) Is Y (t) wide sense stationary?
(b) Is Y (t) a Gaussian random process?