**Problem (12): Let X1, X2 be a random sample of size n = 2 from the exponentialprobability density function (pdf) with an unknown parameter 0 given as follows:f(x; 0) = }e, x>0; 0>0otherwiseConsider the following two estimators for the unknown parameter 0:6, = T,(X1, X2) = X4Ô2 = T2(X1, X2) = -X,X2then show that ê, is more efficient than Ô, for estimating 0?

Given information: Given that the random sample X1, X2, … ,Xn is from an exponential distribution…

Answered: Let X1, X2 be a random sample of size n…

Let X1, X2 be a random sample of size n : = 2 from the exponential ity function (pdf with an unknown parameter 0 given as follows: x> 0; 0>0 f(r:A)

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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**Problem (12): Let X1, X2 be a random sample of size n = 2 from the exponential
probability density function (pdf) with an unknown parameter 0 given as follows:
f(x; 0) = }e
, x>0; 0>0
otherwise
Consider the following two estimators for the unknown parameter 0:
6, = T,(X1, X2) = X
4
Ô2 = T2(X1, X2) = -X,X2
then show that ê, is more efficient than Ô, for estimating 0?

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