Y; = Bx; + €;, i = 1, ..., n. here ¤1,..., xn are fixed constants, and e; are i.i.d. random variables that follow N(0, o²) wl 2 is unknown. (a) Is 3 = EYi/Ex; an unbiased estimator of B? Show work. (b) Find the variances of B and ß. If you already found the variance of 3 from Problem 3 then yo don't need to find it again. Which estimator has smaller variance? Which estimator is a bette estimator? And why? Show work.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
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3. Consider the random variables Y1,..., Yn that satisfy
Y; = Bx; + €;, i = 1, ..., n.
where x1,..., Xn are fixed constants, and e; are i.i.d. random variables that follow N(0, o²) where
o2 is unknown.
(a) Is B = EYi/Ex; an unbiased estimator of B? Show work.
(b) Find the variances of 3 and ß. If you already found the variance of 3 from Problem 3 then you
don't need to find it again. Which estimator has smaller variance? Which estimator is a better
estimator? And why? Show work.
Transcribed Image Text:3. Consider the random variables Y1,..., Yn that satisfy Y; = Bx; + €;, i = 1, ..., n. where x1,..., Xn are fixed constants, and e; are i.i.d. random variables that follow N(0, o²) where o2 is unknown. (a) Is B = EYi/Ex; an unbiased estimator of B? Show work. (b) Find the variances of 3 and ß. If you already found the variance of 3 from Problem 3 then you don't need to find it again. Which estimator has smaller variance? Which estimator is a better estimator? And why? Show work.
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