Let the sample functions of a random process be given by

X(t) = A cos 2Ï€f₀t

where ω₀ is fixed and A has the pdf 

This random process is passed through an ideal integrator to give a random process Y(t).

(a) Find an expression for the sample functions of the output process Y(t).

(b) Write down an expression for the pdf of Y(t) at time t₀. Note that sin 2Ï€f₀t₀ is jsut a constant. 

(c) Is Y(t) stationary? Is it ergodic?

Transcribed Image Text:

e-a? /20, fA (a) = V2πσ, τσ α