WebWork-03: Problem 2 Previous Problem List Next Suppose Z, is white noise with

Question

WebWork-03: Problem 2 Previous Problem List Next Suppose Z, is white noise with mean zero. Define the stochastic process (X,1,1,2,3... by Consider a sample X1, X2, , X200 taken from {%) on 200 consecutive time points. Let the mean of these observations be X. Part a) Suppose = 0.665. Compared to the sample mean of a sample of size 200 taken at random from a random variable with the same variance as X,X will have A. the same variance. B. higher variance. C. lower variance. Part (b) Compared to the sample mean of a sample of size 100 taken at random from a random variable with the same variance as (x,], X will have A. lower variance. B. higher variance. C. the same variance. Part (c) Now suppose =-0.56. Compared to the sample mean of a sample of size 200 taken at random from a random variable with the same variance as (X,)X wil have A. the same variance. B. lower variance. C. higher variance.

Explanation / Answer

Part a) The variance is not change becaause the sample size as well as coefficient of X does not change

So correct answer of this part is A

part b) When we reduce sample size then the variance of sample mean increases.

So that the correct choice of this part is B

part c) This is the autoregressive model so that the variance decreases as | a | decreases

So correct answer is B.

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