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Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t ≤ R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims o E [X(0)(X(t+8) − X(t))] = 0 for all t. Use the Schwarz inequality.

Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t ≤ R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims o E [X(0)(X(t+8) − X(t))] = 0 for all t. Use the Schwarz inequality.

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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Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t e R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims→0 E[X(0)(X(t+8) – X(t))] = 0 for all t. Use the Schwarz inequality.
Transcribed Image Text:Exercise 3.25 Let Kx(t) be the covariance function of a WSS process {X(t); t e R}. Show that if Kx(t) is continuous at t = 0, then it is continuous everywhere. Hint: You must show that lims→0 E[X(0)(X(t+8) – X(t))] = 0 for all t. Use the Schwarz inequality.
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