Question 1: (The random Telegraph Signal Process) Let {N(!), 2 0} denote a Poisson process with rate 1, and let X, be in

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Question 1 The Random Telegraph Signal Process Let N 2 0 Denote A Poisson Process With Rate 1 And Let X Be In 1 (37.06 KiB) Viewed 22 times

Question 1: (The random Telegraph Signal Process) Let {N(!), 2 0} denote a Poisson process with rate 1, and let X, be independent of this process and be such that P{X, = 1} = P{X= -1} 2 Defining X(t) = X(-1)(1) then {X(t), t 2 0} is called a random telegraph signal process. To see that it is stationary, note first that starting at any time t, no matter what the value of N(!), as X, is equally likely to be either plus or minus I.it follows that X(t) is equally likely to be either plus or minus 1. Hence, because the continuation of a Poisson process beyond any time remains a Poisson process, it follows that {X(t),t 0} is a stationary process. 1. Calculate E[X] and Var[X] 2. Compute E[X] the mean function of the random telegraph signal. 3. Compute Cov[X(t),X(t + s)] the covariance function of the random telegraph signal.