Let X (t) be a wide sense stationary random process that is ergodic in the mean and the autocorrelation. However, X (t) is not zero- mean. Let Y (t) = CX (t), where C is a random variable independent of X (t) and C is not zero- mean. Show that Y (t) is not ergodic in the mean or the autocorrelation.
Answer to relevant QuestionsLet X (t) be a WSS random process with mean uX and autocorrelation function RXX ( r ). Consider forming a new process according to a) Find the mean function of Y (t). b) Find the autocorrelation function of Y (t). Is Y (t) ...Suppose X (t) is a Weiner process with diffusion parameter λ = 1 as described in Section 8.5. (a) Write the joint PDF of X1 = X (t1) and X2 = X (t2) for t2 < t1 by evaluating the covariance matrix of X = [X1, X2] T and ...Let, Xi (t) i = 1, 2… n, be a sequence of independent Poisson counting processes with arrival rates,λi. Show that the sum of all of these Poisson processes, Is itself a Poisson process. What is the arrival rate of the sum ...Suppose the power line in the previous problem has an impulse response that may be approximated by h (t) = te– atu (t), where a = 10s– 1. (a) What does the shot noise on the power line look like? Sketch a possible ...A random process X (t) consists of three- member functions: x1 (t) = 1 x2 (t) = – 3, and x3(t) = sin (2πt). Each member function occurs with equal probability. (a) Find the mean function, µX (t). (b) Find the ...
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