(adsbygoogle = window.adsbygoogle || []).push({}); 1. (Form 1) X_t = A cos(λt +φ ) ,

where φ was Unif [−pi ,pi ] , λ is a fixed constant and A is a constant (or a RV mean 0,

variance \σ^\2_\A, and indep of φ ). ]

Now consider the following: Let B_1 , B_2 be IID Normal(0,\σ^\2_\B) and λ a fixed constant

(Form 2) Y_t = B_1 cos(λ_t) + B2 sin(λ_t)

Can Form 2 be written in a manner similar to Form 1? If so, show how.

[Hint: you know the distribution of {\frac{\-B_2}{B_1}}

(Cauchy). Define

φ = arctan({\frac{\-B_2}{B_1}}) . What is the distribution of φ ?]

I am lost in what I need to do. Could someone give me some help? Or some hint?

Thanks!

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# Homework Help: Question on time series/cauchy distribution

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