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in = E=1 Xk. Show that if we further have a finite variance, i. Sa 3 µ. In other words, Sn lim ||- Sn lim Var(") = 0. n-00 n00

in = E=1 Xk. Show that if we further have a finite variance, i. Sa 3 µ. In other words, Sn lim ||- Sn lim Var(") = 0. n-00 n00

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose that {Xk} is an i.i.d. random process with finite mean E[X;] = µ. By the strong law of large numbers we know that Sn lim =µ a.s., where S, = E, Xg. Show that if we further have a finite variance, i.e., Var(Xr) = o² < o, then lim,→0 Sa 3 µ. In other words, Sn lim ||- Sn - H||? = lim Var(-"). 0. n00 00u This is known as the weak law of large numbers.
Transcribed Image Text:Suppose that {Xk} is an i.i.d. random process with finite mean E[X;] = µ. By the strong law of large numbers we know that Sn lim =µ a.s., where S, = E, Xg. Show that if we further have a finite variance, i.e., Var(Xr) = o² < o, then lim,→0 Sa 3 µ. In other words, Sn lim ||- Sn - H||? = lim Var(-"). 0. n00 00u This is known as the weak law of large numbers.
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