Answered: 5-2. Suppose that X1, X2, ... are IID… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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5-2. Suppose that X1, X2, ... are IID random variables. For some subset
A of the real numbers, define
Y; = IA(X¡),
i = 1,2,...
and
Yn
Yi.
Show that Y, converges in probability to Pr(X; € A), and in fact
Yn – Pr(X; € A) = Op(n¬1/2).
-
Also show that Yn is the fraction of X1, ..., Xn that lie in A.

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