Let X1, X2, ... X be a random sample from a population with the following probability density function; x> 0 f(x;0) = elsewhere. In order to estimate the parameter 0, two estimators have been proposed; T = X, and T2 = nX(1) where X, is the sample mean and X(1) = min {X1,X2, ...Xn}. Calculate the mean and the variance of the estimators T, and T2 Calculate the mean squared error of the estimators T1 and T2 Show that Var(T,) s Var(T2). Why?

Let X1, X2, ... X be a random sample from a population with the following probability density function; x> 0 f(x;0) = elsewhere. In order to estimate the parameter 0, two estimators have been proposed; T = X, and T2 = nX(1) where X, is the sample mean and X(1) = min {X1,X2, ...Xn}. Calculate the mean and the variance of the estimators T, and T2 Calculate the mean squared error of the estimators T1 and T2 Show that Var(T,) s Var(T2). Why?

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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Question

Let X1, X2, ... X be a random sample from a population with the following probability
density function;
x> 0
f(x;0) =
elsewhere.
In order to estimate the parameter 0, two estimators have been proposed;
T = X, and T2 = nX(1)
where X, is the sample mean and X(1) = min {X1,X2, ...Xn}.
Calculate the mean and the variance of the estimators T, and T2
Calculate the mean squared error of the estimators T1 and T2
Show that Var(T,) s Var(T2). Why?

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