3. Consider the random variables Y1,..., Yn that satisfyY; = Bx; + €;, i = 1, ..., n.where x1,..., Xn are fixed constants, and e; are i.i.d. random variables that follow N(0, o²) whereo2 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 youdon't need to find it again. Which estimator has smaller variance? Which estimator is a betterestimator? And why? Show work.

Name: 3. Consider the random variables Y1,..., Yn that satisfyY; = Bx; + €;
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Description: 3. Consider the random variables Y1,..., Yn that satisfyY; = Bx; + €;, i = 1, ..., n.where x1,..., Xn are fixed constants, and e; are i.i.d. random variables that follow N(0, o²) whereo2 is unknown.(a) Is B = EYi/Ex; an unbiased estimator of B? Show

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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.

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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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.

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