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2. Let X₁ X₂, X, bve a random sample of size 3 selected from a population with probability density (pdf) given by f(x 0) 0ex, x>0, 0>0. a. Show that Y = X₁ + X₂ + X, is a complete sufficient statistic for 0. b. Define 2 h(X₁, X₂, X₁)=1-e₁ i) Show that h(X₁, X₂, X,) is an unbiased estimator of r(0)= ii) Let us assume that the distribution of X, |Y=y has a pdf 2 f(x, y) = 3 / (v (v-x) for 0≤x, sy. Find the uniform minimum variance unbiased estimator (UMVUE) of r(0). 1+0

2. Let X₁ X₂, X, bve a random sample of size 3 selected from a population with probability density (pdf) given by f(x 0) 0ex, x>0, 0>0. a. Show that Y = X₁ + X₂ + X, is a complete sufficient statistic for 0. b. Define 2 h(X₁, X₂, X₁)=1-e₁ i) Show that h(X₁, X₂, X,) is an unbiased estimator of r(0)= ii) Let us assume that the distribution of X, |Y=y has a pdf 2 f(x, y) = 3 / (v (v-x) for 0≤x, sy. Find the uniform minimum variance unbiased estimator (UMVUE) of r(0). 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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2. Let X₁, X₂, X, bve a random sample of size 3 selected from a population with probability density (pdf) given by f(x 0) 0e, x>0, 0>0. a. Show that Y = X₁ + X₂ + X, is a complete sufficient statistic for 0. b. Define h(X₁, X₂, X₂)=1-e₁ i) Show that h(X₁, X₁, X,) is an unbiased estimator of r(0)= ii) Let us assume that the distribution of X₁ Y =y has a pdf 2 f(x, y) = (v-x) for 0≤x, sy. Find the uniform minimum variance unbiased estimator (UMVUE) of r(0). 1+0
Transcribed Image Text:2. Let X₁, X₂, X, bve a random sample of size 3 selected from a population with probability density (pdf) given by f(x 0) 0e, x>0, 0>0. a. Show that Y = X₁ + X₂ + X, is a complete sufficient statistic for 0. b. Define h(X₁, X₂, X₂)=1-e₁ i) Show that h(X₁, X₁, X,) is an unbiased estimator of r(0)= ii) Let us assume that the distribution of X₁ Y =y has a pdf 2 f(x, y) = (v-x) for 0≤x, sy. Find the uniform minimum variance unbiased estimator (UMVUE) of r(0). 1+0
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