# Question: Suppose Xk is a sequence of zero mean Gaussian random

Suppose Xk is a sequence of zero- mean Gaussian random variables with co-variances described by Cov (Xk, Xm) =ρ |k– m| for some |ρ| < 1. Form the sequence of sample means

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.

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.

**View Solution:**## Answer to relevant Questions

Suppose, X1, X2, Xn, is a sequence of IID positive random variables. Define Show that as n →∞, yn converges in distribution, and find the distribution to which it converges. Let, Xk k = 1, 2, 3… be a sequence of IID Cauchy random variables with and let Sn be the sequence of sample means, (a) Show that also follows a Cauchy distribution. (b) Prove that in this case, the sample mean does not ...Suppose we wish to estimate the probability, PA, of some event A as outlined .As motivated by the result, suppose we repeat our experiment for a random number of trials, N. In particular, we run the experiment until we ...Let be a random sum of discrete IID random variables. Further, let HN (z) and HX (z) be the probability- generating functions of N and X, respectively. Find the probability- generating function of S assuming that N is ...Show that if Xn ,n = 1, 2, 3, … is a sequence of IID Gaussian random variables, the sample mean and sample variance are statistically independent.Post your question