Example 15: Consider a random process X, (t) = A X (t) cos (@e t + 0) where X (t) iszero mean, stationary random process. X (t) and 0 are assumed to be independent.A and w. are constants. e is a random variable uniformly distributed in the interval(- T , T). Show that X. (t) is WSS process.

Answered: Image /qna-images/answer/587eb6e3-b61f-4732-a2ee-54e2ed757e6d.jpg

Answered: Example 15: Consider a random process…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A random process is defined by X(t) = X₁ + Vt where X and V are statistically independent random variables uniformly distributed on intervals [X01, X02] and [V1, V2], respectively. Finds tion, , (b) the autocorrela-
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Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)
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The autocorrelation of a WSS random process X(t) is given by Rxx (T) = Acos(@,t) XX where A and w, are constants. Find psd.
Which of the following could be the correlation function of a stationary random process? (a) R(t) = exp(-7). (d) R(T) = sin(7). (b) R,(t) exp(-г)и( г). (e) R(7) = cos (r). %3D (c) R (7) = exp(l1). (f) R(7) = sinc(7). %3D
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Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
Example 7: Given that the random process X (t) = 10 cos (100t + 0) where 1s a uniformly distributed random variable in the interval (-1 , T). Show that the process is correlation-ergodic. %3D
Q. 3 Let continuous random variables X and Y be independent identically distributed random variables with the following respective pdfs: fx(x) = 2e-2x;x 2 0 and fy (y) = 2e-2y;y > 0 Define a new random variable Z = X + Y. Derive moment generating function of Z, i.e. Mz(t).

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Example 15: Consider a random process X, (t) = A X (t) cos (@e t + 0) where X (t) is zero mean, stationary random process. X (t) and 0 are assumed to be independent. A and w. are constants. e is a random variable uniformly distributed in the interval (- T , T). Show that X. (t) is WSS process.