Let Y,, Y2, Y3, and Y, be independent, identically distributed random variables from a population with mean u and variance o?. Let Y = -(Y, + Y, + Y, + Y4) denote the average of these four random variables. (i) What are the expected value and variance of Y in terms of u and o²? (ii) Now, consider a different estimator of µ: W = -Y, Y, + *A + 1? + + This is an example of a weighted average of the Y,. Show that W is also an unbiased estimator of u. Find the variance of W. (iii) Based on your answers to parts (i) and (ii), which estimator of m do you prefer, Y or W?
Let Y,, Y2, Y3, and Y, be independent, identically distributed random variables from a population with mean u and variance o?. Let Y = -(Y, + Y, + Y, + Y4) denote the average of these four random variables. (i) What are the expected value and variance of Y in terms of u and o²? (ii) Now, consider a different estimator of µ: W = -Y, Y, + *A + 1? + + This is an example of a weighted average of the Y,. Show that W is also an unbiased estimator of u. Find the variance of W. (iii) Based on your answers to parts (i) and (ii), which estimator of m do you prefer, Y or W?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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
Transcribed Image Text:Let Y,, Y2, Y3, and Y, be independent, identically distributed random variables from a population with
mean u and variance o?. Let Y = -(Y, + Y, + Y, + Y4) denote the average of these four random
variables.
(i) What are the expected value and variance of Y in terms of u and o²?
(ii) Now, consider a different estimator of µ:
W = -Y,
Y, +
*A + 1? + +
This is an example of a weighted average of the Y,. Show that W is also an unbiased estimator of
u. Find the variance of W.
(iii) Based on your answers to parts (i) and (ii), which estimator of m do you prefer, Y or W?
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