Using a long rod that has length μ, you are going to lay out a square plot in which the length of each side is μ. Thus the area of the plot will be μ2 However, you do not know the value of μ, so you decide to make n independent measurements X1, X2,..., Xn of the length.Assume that each Xi has mean μ (unbiased measurements) and variance σ2. a. Show that X2 is not an unbiased estimator for u?. [Hint: For anyrv Y, E(Y) = V(Y) + [E{Y)]°. Apply this with Y= X.]b. For what value of kis the estimator X2 - ks unbiased for u??[Hint: Compute E( X - ks²).]

If an expected value of sample statistic is equals to the population parameter then that…

a. Show that X2 is not an unbiased estimator for u?. [Hint: For any rv Y, E(Y) = V(Y) + [E{Y)]°. Apply this with Y= X.] b. For what value of kis the estimator X2 - ks unbiased for u?? [Hint: Compute E( X - ks²).]

a. Show that X2 is not an unbiased estimator for u?. [Hint: For any rv Y, E(Y) = V(Y) + [E{Y)]°. Apply this with Y= X.] b. For what value of kis the estimator X2 - ks unbiased for u?? [Hint: Compute E( X - ks²).]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 32T

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Question

Using a long rod that has length μ, you are going to lay out a square plot in which the length of each side is μ. Thus the area of the plot will be μ²
However, you do not know the value of μ, so you decide to make n independent measurements X₁, X₂,..., X_n of the length.
Assume that each Xi has mean μ (unbiased measurements) and variance σ².

a. Show that X2 is not an unbiased estimator for u?. [Hint: For any
rv Y, E(Y) = V(Y) + [E{Y)]°. Apply this with Y= X.]
b. For what value of kis the estimator X2 - ks unbiased for u??
[Hint: Compute E( X - ks²).]

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