# Question: Let X t be a modified version of the random

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?

(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?

**View Solution:**## Answer to relevant Questions

Let s (t) be a periodic square wave as illustrated in the accompanying figure. Suppose a random process is created according to X (t) = s (t – T), where T is a random variable uniformly distributed over (0, 1). (a) Find ...Let 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 ...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- ...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 ...A shot noise process with random amplitudes is defined by Where the Si are a sequence of points from a Poisson process and the Ai are IID random variables which are also independent of the Poisson points. (a) Find the mean ...Post your question