Let X1, ..., Xn be a random sample from N(μ, σ2), where σ2 is known. a) Show that Y = (X1 + X2)/2 is an unbiased estimator of μ. b) Find the Cramer-Rao lower bound for the variance of an unbiased estimator of μ for a general n. c) What is the efficiency of Y in part (a) above?

Let X1, ..., Xn be a random sample from N(μ, σ2), where σ2 is known. a) Show that Y = (X1 + X2)/2 is an unbiased estimator of μ. b) Find the Cramer-Rao lower bound for the variance of an unbiased estimator of μ for a general n. c) What is the efficiency of Y in part (a) above?

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, ..., Xn be a random sample from N(μ, σ2), where σ2
is known.
a) Show that Y = (X1 + X2)/2 is an unbiased estimator of μ.
b) Find the Cramer-Rao lower bound for the variance of an unbiased
estimator of μ for a general n.
c) What is the efficiency of Y in part (a) above?

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