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4a. Consider a RP X(t) = Acos (wot + 0). Let A and 0 are independent and follows uniform distributions with A: U(0,10) and 8: U(0, 2). Is the process i) Ergodic in the mean? ii) Ergodic with respect to the RMS value?

4a. Consider a RP X(t) = Acos (wot + 0). Let A and 0 are independent and follows uniform distributions with A: U(0,10) and 8: U(0, 2). Is the process i) Ergodic in the mean? ii) Ergodic with respect to the RMS value?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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4a. Consider a RP X(t) = Acos (wot+0). Let A and are independent and follows uniform distributions with A: U(0,10) and 8: U(0, 2n). Is the process i) Ergodic in the mean? ii) Ergodic with respect to the RMS value? 4b. A WSS Gaussian RP has mean E[X(t)]=2, and covariance function Cx (T) = 8 сos(T). Two random variables are taken at times as shown below Xi(t=0); X₂(1=0.5); i) Find the covariance matrix for X, and X2. ii) Write the second-order probability density function for RVs X₁ and X₂.
Transcribed Image Text:4a. Consider a RP X(t) = Acos (wot+0). Let A and are independent and follows uniform distributions with A: U(0,10) and 8: U(0, 2n). Is the process i) Ergodic in the mean? ii) Ergodic with respect to the RMS value? 4b. A WSS Gaussian RP has mean E[X(t)]=2, and covariance function Cx (T) = 8 сos(T). Two random variables are taken at times as shown below Xi(t=0); X₂(1=0.5); i) Find the covariance matrix for X, and X2. ii) Write the second-order probability density function for RVs X₁ and X₂.
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