Question: (I'm taking Random Processes class) Let X n = Z n-1 + Z n and n = 1, 2, 3... where Z 0 , Z

(I'm taking Random Processes class)

Let Xn = Zn-1 + Zn and n = 1, 2, 3...

where Z0, Z1, Z2... are I.I.D. ~N(0,1).

Let Yn = Xn-1 + Xn and n = 2,3,4...

Find the mean and autocorrelation functions of Yn

For the mean, I found that Yn = Zn + 2*Zn-1 + Zn-2

So, E[Yn] = E[Zn + 2*Zn-1 + Zn-2] = 0

For the autocorrelation, I got

RY(n1,n2) = E[Yn1 * Yn2] = E[(Zn1 + 2*Zn1-1 + Zn1-2)*(Zn2 + 2*Zn2-1 + Zn2-2)]=....

I got lost here.

Can any of you guys help me out to find the autocorrelation from here?

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