Let X (t) and X (t) be two jointly wide sense stationary Gaussian random processes with zero- means and with autocorrelation and cross- correlation functions denoted as , RXY (r), and RXY (r). Determine the cross- correlation function between X2 (t) and Y2 (t)
Answer to relevant QuestionsSuppose 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 ...Consider a Poisson counting process with arrival rate λ. (a) Suppose it is observed that there is exactly one arrival in the time interval [0, to]. Find the PDF of that arrival time. (b) Now suppose there were exactly two ...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 N (t) be a Poisson counting process with arrival rate, λ. Determine whether or not N (t) is mean square continuous. A square matrix is called a stochastic matrix if all of its elements satisfy 0= pi, j = 1 and, furthermore for all i. Every stochastic matrix is the transition probability matrix for some Markov chain; however, not every ...
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