Two zero- mean discrete- time random processes, X [n] and Y [n], are statistically independent. Let a new random process be Z [n] = X [n] + Y [n]. Let the autocorrelation functions for X [n] and X [n] be
Find RZZ [k]. Plot all three autocorrelation functions (you may want to use MATLAB to help).
Answer to relevant QuestionsLet Wn be an IID sequence of zero- mean Gaussian random variables with variance . Define a discrete- time random process, X[ n] = pX[ n – 1]+ Wn, n = 1, 2, 3, … where X[ 0] = W0 and is a constant. (a) Find the mean ...A stationary random process, X (t), has a mean of μX and correlation function, RX, X (t). A new process is formed according to Y (t) = aX (t) + b for constants and. Find the correlation function in terms of μX and R X,X ...Prove that the family of differential equations, leads to the Poisson distribution, Define a random process according to X[n] = X [n– 1] + Wn , n = 1, 2, 3, … Where X  = 0 and Wn is a sequence of IID Bernoulli random variables with and Pr( Wn = 1)= p and Pr( Wn = 0) = 1 – p. (a) Find the PMF, PX ...Let X (t) be a Weiner process with diffusion parameter λ as described in Section 8.5. Determine whether or not X (t) is mean square continuous.
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