Let Y₁, Y₂, and Y be independent, identically distributed random variables from a population with mean μ and variance o². Let Y = (Y₁+Y₂+Y.) denote the average of these four random variables. a. What are the expected value and variance of Y in terms of μ and o²? b. Now, consider an estimator of μ: C. ²1/11/₂2-² + W=Y₁ + 1 This is an example of a weighted average of the Y's. Show that W is also an unbiased estimator of μ. Find the variance of W. Based on your answers in (a) and (b), which estimator of μ do you prefer, Y or W?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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3.
Let Y₁, Y₂, and Y be independent, identically distributed random variables from a
2'
population with mean μ and variance o². Let Y = (Y,+Y+Y₂) denote the average of these
four random variables.
What are the expected value and variance of Y in terms of μ and o²?
b. Now, consider an estimator of μ:
a.
C.
W = = Y ₁²
+
+
3 2 9 3
This is an example of a weighted average of the Y's. Show that W is also an
unbiased estimator of μ. Find the variance of W.
Based on your answers in (a) and (b), which estimator of μ do you prefer, Y or W?
Transcribed Image Text:3. Let Y₁, Y₂, and Y be independent, identically distributed random variables from a 2' population with mean μ and variance o². Let Y = (Y,+Y+Y₂) denote the average of these four random variables. What are the expected value and variance of Y in terms of μ and o²? b. Now, consider an estimator of μ: a. C. W = = Y ₁² + + 3 2 9 3 This is an example of a weighted average of the Y's. Show that W is also an unbiased estimator of μ. Find the variance of W. Based on your answers in (a) and (b), which estimator of μ do you prefer, Y or W?
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