Question: Suppose Xk is a sequence of zero- mean Gaussian random variables with co-variances described by Cov (Xk, Xm) =Ï |k m| for some |Ï| In

Suppose Xk is a sequence of zero- mean Gaussian random variables with co-variances described by Cov (Xk, Xm) =Ï |k€“ m| for some |Ï|

In this case we are forming the sequence of sample means of dependent random variables.
(a) Determine if the sequence Sn converges in distribution.
(b) Determine if the sequence Sn converges in probability.
(c) Determine if the sequence Sn converges in the MS sense.

Sn = .rk , n = 1, 2, 3,-. k= 1

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