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5. Let X₁, X2,..., Xn be a random sample from a population with the probability density function x² exp 20 2 f(x) = πθ You may assume that E(X²) = 0 and Var(X²) = 20. ΣX² i=1 = 0

5. Let X₁, X2,..., Xn be a random sample from a population with the probability density function x² exp 20 2 f(x) = πθ You may assume that E(X²) = 0 and Var(X²) = 20. ΣX² i=1 = 0

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. Let X₁, X2, ..., Xn be a random sample from a population with the probability density function x² 20 2 no-Vine's -exp f(x) пө You may assume that E(X²) = 0 and Var (X²) = 20. n X? 0<u<2 otherwise (a) Show that the estimator = is an unbiased estimator for 0. n (b) Show that the Cramer-Rao Lower Bound is attained for this estimator.
Transcribed Image Text:5. Let X₁, X2, ..., Xn be a random sample from a population with the probability density function x² 20 2 no-Vine's -exp f(x) пө You may assume that E(X²) = 0 and Var (X²) = 20. n X? 0<u<2 otherwise (a) Show that the estimator = is an unbiased estimator for 0. n (b) Show that the Cramer-Rao Lower Bound is attained for this estimator.
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