Let X (t) be a modified version of the random telegraph process The process switches between the two states X (t) 1 and X (t) 1 with the time between switches following exponential distributions, fT (s) exp (s) u (s) Also, the starting state is determined by flipping a biased coin so that Pr(X (0) 1) p and Pr (X (0) 1) 1 p (a) Find and Pr(X (t) 1) and Pr (X (t) 1) (b) Find the mean function, X (t) (c) Find the autocorrelation function, RX, X (t1, t2) (d) Is this process WSS

Question: Let X (t) be a modified version of the random telegraph process. The process switches between the two states X (t) = 1 and X

Let X (t) be a modified version of the random telegraph process. The process switches between the two states X (t) = 1 and X (t) = –1 with the time between switches following exponential distributions, fT (λs) = λexp (–λs) u (s). Also, the starting state is determined by flipping a biased coin so that Pr(X (0) = 1) = p and Pr (X (0) = – 1) = 1 – p.
(a) Find and Pr(X (t) = 1) and Pr (X (t) = – 1).
(b) Find the mean function, µX (t).
(c) Find the autocorrelation function, RX, X (t1, t2).
(d) Is this process WSS?

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