1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean: ˆμ1 = (n −3/n) ̄X ˆμ2 = 0.95 ̄X (a) Which of the estimators is an unbiased estimator for μ? (b) Which is the variance of the two estimators? (c) Given the properties above, which one would you prefer? Is there another property that would influence your decision? Explain.
1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean: ˆμ1 = (n −3/n) ̄X ˆμ2 = 0.95 ̄X (a) Which of the estimators is an unbiased estimator for μ? (b) Which is the variance of the two estimators? (c) Given the properties above, which one would you prefer? Is there another property that would influence your decision? Explain.
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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1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ
and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean:
ˆμ1 = (n −3/n) ̄X
ˆμ2 = 0.95 ̄X
(a) Which of the estimators is an unbiased estimator for μ?
(b) Which is the variance of the two estimators?
(c) Given the properties above, which one would you prefer? Is there another property that would
influence your decision? Explain.
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