Question: Problem 7.6 Consider the following difference equation with initial condition X (0) = 1 and U(n), n 2 0 a sequence of zero mean, uncorrelated




Problem 7.6 Consider the following difference equation with initial condition X (0) = 1 and U(n), n 2 0 a sequence of zero mean, uncorrelated Gaussian random variables with variance 0%,. X(n+1)=\\/EX(n)+U(n), n=0,1,2,... (a) Find mr(n). (b) Find Rx (0, k), Rx (1, 1), Rx (1, 2), and Rx (3, 1). (c) Develop a recursive expression for the variance of X (n). (d) Is the variance of X(n) bounded as n grows to infinity? Explain
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