1. A random process is an infinite indexed collection of random variables. Here we will consider...

 

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1. A random process is an infinite indexed collection of random variables. Here we will consider one specific example of a random process in which the random variables are indexed by the integers, specifically, the random process {X(n), n e Z}. The process that we consider is called a first-order Gauss-Markov random process, and it is defined in terms of another random process {W(n), ne Z} by the equation X(n) = pX(n-1) + W(n), n =..., -2, -1,0, 1, 2,... Here p ER, -1 < p < 1, all the random variables X(n) and W(n) are assumed to be zero-mean, all the W(n) are mutually independent and W(n) is independent of X(m), m 1. A random process is an infinite indexed collection of random variables. Here we will consider one specific example of a random process in which the random variables are indexed by the integers, specifically, the random process {X(n), n e Z}. The process that we consider is called a first-order Gauss-Markov random process, and it is defined in terms of another random process {W(n), ne Z} by the equation X(n) = pX(n-1) + W(n), n =..., -2, -1,0, 1, 2,... Here p ER, -1 < p < 1, all the random variables X(n) and W(n) are assumed to be zero-mean, all the W(n) are mutually independent and W(n) is independent of X(m), m

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A Show that oxn poxn1own 02 is the variance of the random variable that appears in its subscript Solution We can calculate the variance of Xn as follo... View the full answer