Define a random process according to X[n] = X [n 1] + Wn , n = 1,
Question:
X[n] = X [n– 1] + Wn , n = 1, 2, 3, …
Where X [0] = 0 and Wn is a sequence of IID Bernoulli random variables with and Pr( Wn = 1)= p and Pr( Wn = 0) = 1 – p.
(a) Find the PMF, PX (k; n) = Pr (X[k] = n).
(b) Find the joint PMF, PX1, X2 (k1, k2 ; n1, n2) = Pr (X [k1] = n1, X [k2] = n2).
(c) Find the mean function, µX [n] = E [X[n]].
(d) Find the autocorrelation function, RX, X [k, n] = E [X [k] X [n]].
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a That X 1 W 1 X 2 X 1 W 2 W 1 W 2 Since the W k are the IID Bernoulli ...View the full answer
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Related Book For 
Probability and Random Processes With Applications to Signal Processing and Communications
ISBN: 978-0123869814
2nd edition
Authors: Scott Miller, Donald Childers
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