Question: This is a question about statistical random process. Let Z 1 , Z 2 , ... be independent random variables with Pr[Z k =1] =

This is a question about statistical random process.

Let Z1, Z2, ... be independent random variables with Pr[Zk=1] = Pr[Zk=-1] ?=21?? ??? k = 1, 2, ......

Define Xt??? ??k=1??? Zk2-ke-it/k????t?R? in the mean square sense, where ?i=??1?

(Note: X is defined to be Y in the mean square sense if ?E[(X?Y)2]=0?

  1. Show that the limit of the sum converges (i.e. Xt is well defined ??? t)
  2. Find Rx(t,s) ??? t, s
  3. Is Xt wide sense stationary?

Please also refer to the image attached to this question. Thanks!

This is a question about statistical random process. Let Z1, Z2, ...

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