Module Code: MATH3802021. (a) Define the terms "strongly stationary" and "weakly stationary".Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} isweakly stationary, define the autocorrelation function (acf) Pk, for lag k.What conditions must a process {X+) satisfy for it to be white noise?(b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which ofthe following processes {X+} are weakly stationary for t> 0? Briefly justify youranswers.i. Xt for all > 0.ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0.(c) Provide an expression for estimating the autocovariance function for a sampleX1,..., X believed to be from a weakly stationary process. How is the autocor-relation function Pk then estimated, and a correlogram (or acf plot) constructed?(d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where{E} is a white noise process with variance 1. Compute the population autocorre-lation function Pk for all k = 0, 1, ....

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Answered: Module Code: MATH380202 1. (a) Define…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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