Suppose X1, X2, X3, X4 be i.i.d. normal random variables with mean 0 and variance o, where o is the unknown parameter. Consider the following estimators: T1 X- X2 + X4, T2 (X? + X3 + X3), T3 E X7, T4 = L(X-X), and T, = |X1- X2l. %3D %3D (a) Is T unbiased for o?, for i = 1,2,3, 4? (b) Among the estimators T,...,T for o, which has the smallest MSE? (c) Is T, unbiased for o? If not, find a constant k so that kT, is unbiased for o. Evaluate the MSE of Ts.
Suppose X1, X2, X3, X4 be i.i.d. normal random variables with mean 0 and variance o, where o is the unknown parameter. Consider the following estimators: T1 X- X2 + X4, T2 (X? + X3 + X3), T3 E X7, T4 = L(X-X), and T, = |X1- X2l. %3D %3D (a) Is T unbiased for o?, for i = 1,2,3, 4? (b) Among the estimators T,...,T for o, which has the smallest MSE? (c) Is T, unbiased for o? If not, find a constant k so that kT, is unbiased for o. Evaluate the MSE of Ts.
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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Suppose X1, X2, X3, X4 be i.i.d. normal random variables with mean 0 and variance sigma^2, where sigma^2 is the unknown parameter.
Consider the following estimators: T1 = X1 - X2 + X4, T2 = 1/3(X1 + X1 + X4), T3... T4... T5 = 1/2|X1 - X2|
(a) Is T1 unbiased for sigma^2, for i = 1,2,3,4
(b) Among the estimators T1,...,T4 for sigma^2, which has the smallest MSE?
(c) Is T5 unbiased for sigma? If not, find a constant k so that k*T5 is unbiased for sigma^2. Evaluate the MSE of T5.
![Suppose X1, X2, X3, X4 be i.i.d. normal random variables with mean 0 and variance o?, where
o is the unknown parameter. Consider the following estimators: T1 X- X2 + X4, T2 =
3(X? + X3 + X3), T3 Ex, T L(X-X), and Ts X1- Xal.
%3D
(a) Is T, unbiased for o?, for i 1,2,3, 4?
(b) Among the estimators T,...,T4 for o?, which has the smallest MSE?
(c) Is T, unbiased for o? If not, find a constant k so that KT, is unbiased for o. Evaluate the MSE
of T3.
%D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F071ad70b-680b-44d6-b888-10a290f238d8%2F8e3afdcc-a4c5-4f99-9a25-054f2d8aae66%2Fdndla3m_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose X1, X2, X3, X4 be i.i.d. normal random variables with mean 0 and variance o?, where
o is the unknown parameter. Consider the following estimators: T1 X- X2 + X4, T2 =
3(X? + X3 + X3), T3 Ex, T L(X-X), and Ts X1- Xal.
%3D
(a) Is T, unbiased for o?, for i 1,2,3, 4?
(b) Among the estimators T,...,T4 for o?, which has the smallest MSE?
(c) Is T, unbiased for o? If not, find a constant k so that KT, is unbiased for o. Evaluate the MSE
of T3.
%D
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