Let (X(t)=A sin (omega t+Phi)), where (A) and (Phi) are independent, non-negative random variables with (Phi) uniformly

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Let $X(t)=A \sin (\omega t+\Phi)$, where $A$ and $\Phi$ are independent, non-negative random variables with $\Phi$ uniformly distributed over $[0,2 \pi]$ and $E(A)<\infty$.

(1) Determine trend, covariance, and correlation function of $\{X(t), t \in(-\infty,+\infty)\}$.

(2) Is the stochastic process $\{X(t), t \in(-\infty,+\infty)\}$ weakly and/or strongly stationary?

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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

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Question Posted: Apr 26, 2024 04:00 PM

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Let (X(t)=A sin (omega t+Phi)), where (A) and (Phi) are independent, non-negative random variables with (Phi) uniformly

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Applied Probability And Stochastic Processes

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