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1. If x₁,x₂,...., X, is a random sample from a population whose pdf is given by 10- 12/25015004+ 21/12 -& f(x₁) = elsewhere a. Show that X is an unbiased estimator of 0 [i.e., E(X) = 0 b]. b. Show that is a consistent estimator of 0 [i.e., var (X) becomes smaller as n becomes large].

1. If x₁,x₂,...., X, is a random sample from a population whose pdf is given by 10- 12/25015004+ 21/12 -& f(x₁) = elsewhere a. Show that X is an unbiased estimator of 0 [i.e., E(X) = 0 b]. b. Show that is a consistent estimator of 0 [i.e., var (X) becomes smaller as n becomes large].

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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1. If x₁,x₂,...., X, is a random sample from a population whose pdf is given by -& f(x₁) = 10 - 12/175x150 + 1/1/2 < elsewhere a. Show that X is an unbiased estimator of 0 [i.e., E(X) = 0 b]. b. Show that is a consistent estimator of 0 [i.e., var (X) becomes smaller as n becomes large].
Transcribed Image Text:1. If x₁,x₂,...., X, is a random sample from a population whose pdf is given by -& f(x₁) = 10 - 12/175x150 + 1/1/2 < elsewhere a. Show that X is an unbiased estimator of 0 [i.e., E(X) = 0 b]. b. Show that is a consistent estimator of 0 [i.e., var (X) becomes smaller as n becomes large].
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