Let X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x < 0 202 and E(X) = 0 (Hint: you may use that e-² za-1dz = Show that E(X) (a – 1)! for every a E N). 1. 2. Show that the statistic (1) n i=1 is an unbiased estimator of 0. 3. Give the definition of a consistent estimator. 4. Show that the estimator 0n given in relation (1) is a consistent estimator of 0. 5. Show that the estimator 0, is a minimum variance estimator of 0. (Hint: use the Cramer-Rao inequality given by 1 var(0) > (Ə ln(f(X;0) nE
Let X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x < 0 202 and E(X) = 0 (Hint: you may use that e-² za-1dz = Show that E(X) (a – 1)! for every a E N). 1. 2. Show that the statistic (1) n i=1 is an unbiased estimator of 0. 3. Give the definition of a consistent estimator. 4. Show that the estimator 0n given in relation (1) is a consistent estimator of 0. 5. Show that the estimator 0, is a minimum variance estimator of 0. (Hint: use the Cramer-Rao inequality given by 1 var(0) > (Ə ln(f(X;0) nE
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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Transcribed Image Text:Let X1, .., Xn be a random sample from a population with 0 unknown and given by the
density
= * itz>0
{
e
f(x; 8)
if x < 0
202 and E(X) = 0 (Hint: you may use that e-² za-1dz =
Show that E(X)
(a – 1)! for every a E N).
1.
2.
Show that the statistic
(1)
n
i=1
is an unbiased estimator of 0.
3.
Give the definition of a consistent estimator.
4.
Show that the estimator 0n given in relation (1) is a consistent estimator of 0.
5.
Show that the estimator 0, is a minimum variance estimator of 0. (Hint: use the
Cramer-Rao inequality given by
1
var(0) >
(Ə ln(f(X;0)
nE
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