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1. Let X₁ = (W₁-1 + Wt + Wt+1), where {W}~WN(0,0²). In other words, X, is a three- point moving average of the white noise series. a) Derive μx (t) and yx (t + h, t). b) Is {X} stationary? Explain.

1. Let X₁ = (W₁-1 + Wt + Wt+1), where {W}~WN(0,0²). In other words, X, is a three- point moving average of the white noise series. a) Derive μx (t) and yx (t + h, t). b) Is {X} stationary? Explain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Let X₁ = (W₁-₁ + W₁ + Wt+1), where {W}~WN(0,0²). In other words, X, is a three- t-1 point moving average of the white noise series. a) Derive µx (t) and yx (t + h, t). b) Is {X} stationary? Explain.
Transcribed Image Text:1. Let X₁ = (W₁-₁ + W₁ + Wt+1), where {W}~WN(0,0²). In other words, X, is a three- t-1 point moving average of the white noise series. a) Derive µx (t) and yx (t + h, t). b) Is {X} stationary? Explain.
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Step 1: Write the given information

Given,

X subscript t equals 1 third open parentheses W subscript t minus 1 end subscript plus W subscript t plus W subscript t plus 1 end subscript close parentheses, where open curly brackets W subscript t close curly brackets tilde W N open parentheses 0 comma space sigma squared close parentheses

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