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1. Consider estimator g(n) = In(1 – În). Is it consistent for g(p)? Why? 2. Find the distribution of n(g(In) – 9(p)) a n → o.

1. Consider estimator g(n) = In(1 – În). Is it consistent for g(p)? Why? 2. Find the distribution of n(g(In) – 9(p)) a n → o.

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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Answer following questions attached.

 

Suppose we observe \( X_1, X_2, \ldots, X_n \overset{iid}{\sim} Ber(p) \) and let \( \bar{X}_n \) be the sample average. Suppose we want to estimate the variance \( g(p) = p(1-p) \). 1. Consider estimator \( g(\bar{y}_n) = \bar{y}_n(1-\bar{y}_n) \). Is it consistent for \( g(p) \)? Why? 2. Find the distribution of \( \sqrt{n}(g(\bar{y}_n) - g(p)) \) as \( n \to \infty \).
Transcribed Image Text:Suppose we observe \( X_1, X_2, \ldots, X_n \overset{iid}{\sim} Ber(p) \) and let \( \bar{X}_n \) be the sample average. Suppose we want to estimate the variance \( g(p) = p(1-p) \). 1. Consider estimator \( g(\bar{y}_n) = \bar{y}_n(1-\bar{y}_n) \). Is it consistent for \( g(p) \)? Why? 2. Find the distribution of \( \sqrt{n}(g(\bar{y}_n) - g(p)) \) as \( n \to \infty \).
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