A stochastic process (SP) X(t) is given by X(t) = Asin(ωt + Φ) where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π. a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2). c) Is X(t) wide sense stationary (WSS)? Justify your answer. Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) = 10e−1 4 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables. d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).

A stochastic process (SP) X(t) is given by X(t) = Asin(ωt + Φ) where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π. a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2). c) Is X(t) wide sense stationary (WSS)? Justify your answer. Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) = 10e−1 4 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables. d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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