2. Let Yt = A+ Bt+ Xt, t20, A ~ N(0, 16), B ~ N(0, 81) and Xt = Xt-1+ Et, Et ~GWN(0, 9), Xo = 0. Assume A, B and Et are independent of each other for...

I'm preparing the exam about "probability distributions" and "stochastic models" and I encountered this exercise from a past exam, so I want to understand it in order to get prepared in case there will be a similar exercise on the test.

Is someone could help me on resolve it? An explanation would be great.

Thanks in advance!

2. Let Yt = A+ Bt+ Xt, t20, A ~ N(0, 16), B ~ N(0, 81) andXt = Xt-1+ Et, Et ~GWN(0, 9), Xo = 0.Assume A, B and Et are independent of each other for all t and define Zt = Y- Yt-1, t > 0.(a) Is {Yt } second order stationary?(b) What is the probability distribution of Y?(c) Is {Zt} second order stationary?(d) Compute the autocorrelation function of {Z.}.(e) What is the probability distribution of Zt?