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9.35 Let Y₁, Y₂,... be a sequence of random variables with E(Y) = µ and V (Y) = o. Notice that the o's are not all equal. a What is E(Y)? b What is V (Y)? c Under what condition (on the o's) can Theorem 9.1 be applied to show that Y,, is a consistent estimator for u?

9.35 Let Y₁, Y₂,... be a sequence of random variables with E(Y) = µ and V (Y) = o. Notice that the o's are not all equal. a What is E(Y)? b What is V (Y)? c Under what condition (on the o's) can Theorem 9.1 be applied to show that Y,, is a consistent estimator for u?

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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**9.35** Let \( Y_1, Y_2, \ldots \) be a sequence of random variables with \( E(Y_i) = \mu \) and \( V(Y_i) = \sigma_i^2 \). Notice that the \( \sigma_i^2 \)'s are not all equal. a. What is \( E(\overline{Y}_n) \)? b. What is \( V(\overline{Y}_n) \)? c. Under what condition (on the \( \sigma_i^2 \)'s) can Theorem 9.1 be applied to show that \( \overline{Y}_n \) is a consistent estimator for \( \mu \)?
Transcribed Image Text:**9.35** Let \( Y_1, Y_2, \ldots \) be a sequence of random variables with \( E(Y_i) = \mu \) and \( V(Y_i) = \sigma_i^2 \). Notice that the \( \sigma_i^2 \)'s are not all equal. a. What is \( E(\overline{Y}_n) \)? b. What is \( V(\overline{Y}_n) \)? c. Under what condition (on the \( \sigma_i^2 \)'s) can Theorem 9.1 be applied to show that \( \overline{Y}_n \) is a consistent estimator for \( \mu \)?
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