Define the bias of 0 as an estimator for the parameter 0.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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2. (a) Define the bias of 0 as an estimator for the parameter 0.
(b) For independent random variables X1, X2,..., Xn, assume that E(X;) = µ and
var(X;) — о?, i % ., п.
= 1, ..
(i) Show that ûn = {(X1+Xn)/2} is an unbiased estimator for u and determine
%3D
its variance.
(ii) Find the relative efficiency of n to the unbiased estimator i2 = X, the
sample mean.
(iii) Is û a consistent estimator for u? Justify your answer.
Transcribed Image Text:2. (a) Define the bias of 0 as an estimator for the parameter 0. (b) For independent random variables X1, X2,..., Xn, assume that E(X;) = µ and var(X;) — о?, i % ., п. = 1, .. (i) Show that ûn = {(X1+Xn)/2} is an unbiased estimator for u and determine %3D its variance. (ii) Find the relative efficiency of n to the unbiased estimator i2 = X, the sample mean. (iii) Is û a consistent estimator for u? Justify your answer.
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