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Let et~IID N(0,1) and define Xt=etet-1. Illustrate that {Xt} is the white noise sequence. This gives the example of the dependent white noise sequence. Two bonus points for rigorously proving Xt and Xt+1 are not independent.

Let Xt=1+et-0.5et-1, t=1,2,3,..., where et~IID N(0,2), variance of et is 2.

a. Calculate the mean of Xt.
b. Calculate the variance of Xt.
c. Determine the correlation between Xt and et-1.

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Category:- Statistics and Probability
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