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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.

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.

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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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.
Transcribed Image Text: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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