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A random sequence Xn is defined by X, = A(n-K) u[n – K] where A and K are statistically independent random variables, and u[·] is a unit step sequence. Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete random variable which takes values equal to -1,0, and 1 with equal probability. (a) Determine the mean sequence µx[n] and plot its values for n = -1,0,1,2,3. (b) Determine the auto-correlation bi-sequence Rx[m,n]. (c) Comment on the stationarity of Xņ.

A random sequence Xn is defined by X, = A(n-K) u[n – K] where A and K are statistically independent random variables, and u[·] is a unit step sequence. Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete random variable which takes values equal to -1,0, and 1 with equal probability. (a) Determine the mean sequence µx[n] and plot its values for n = -1,0,1,2,3. (b) Determine the auto-correlation bi-sequence Rx[m,n]. (c) Comment on the stationarity of Xņ.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A random sequence X, is defined by X, = A"-K) u[n – K] where A and K are statistically independent random variables, and u[·] is a unit step sequence. Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete random variable which takes values equal to –1, 0, and 1 with equal probability. (a) Determine the mean sequence µx[n] and plot its values for n= –1,0,1,2,3. (b) Determine the auto-correlation bi-sequence Rx[m, n). (c) Comment on the stationarity of Xn.
Transcribed Image Text:A random sequence X, is defined by X, = A"-K) u[n – K] where A and K are statistically independent random variables, and u[·] is a unit step sequence. Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete random variable which takes values equal to –1, 0, and 1 with equal probability. (a) Determine the mean sequence µx[n] and plot its values for n= –1,0,1,2,3. (b) Determine the auto-correlation bi-sequence Rx[m, n). (c) Comment on the stationarity of Xn.
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