Question: P5.8 | A random sequence X, is defined by X, = Asin(On), n 2 0, in which A and 2 are discrete random variables described

P5.8 | A random sequence X, is defined by X, = Asin(On), n 2 0, in which A and 2 are discrete random variables described by their joint probability mass function (pmf) 1/5, a=w=0 1/5, a=1,w=1/2 1/5, a =1,w=-1/2 PA,n(a,w) = 1/5, a=-1,w =1/2 1/5, a=-1,w=-1/2 0, otherwise Determine: (a) the marginal density f3(x), (b) the joint density fi,s(x, y), c) the mean sequence ux(n), (d) the auto-correlation bi-sequence Rx(m, n), and (e) whether the sequence Xn is . a strict-sense stationary, . a wide-sense stationary, EECE-3468 : HOMEWORK-5 SOLUTIONS : 2021-SMO1 3 an independent random sequence, . an uncorrelated random sequence, and . an orthogonal random sequence. Answers: : (a) -6(x)+6(x+1)+36(x-1), (b) fis(x,y) = $6(x, y)+36(x+1,y+1)+36(x-1,y-1), (c) 0, (d) = sin , ) sin (2")

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