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Let X1,., X, denote a random sample from the uniform distribution on the interval (0,0 + 1). Let 1 ô, = X - and ê2= Y, - 2' n+1' where Y, is the nth order statistic of X1, ..., Xn, i.e., Yn = max(X1,..., Xn). %3D (a) Show that both 6, and ê, are unbiased estimators of 0. (b) Find the efficiency of 6 relative to 02.

Let X1,., X, denote a random sample from the uniform distribution on the interval (0,0 + 1). Let 1 ô, = X - and ê2= Y, - 2' n+1' where Y, is the nth order statistic of X1, ..., Xn, i.e., Yn = max(X1,..., Xn). %3D (a) Show that both 6, and ê, are unbiased estimators of 0. (b) Find the efficiency of 6 relative to 02.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let X1,., Xn denote a random sample from the uniform distribution on the interval (0,0 + 1). Let 1 n n, = X – and Ô2 = Yn - 2' n+1' where Y, is the nth order statistic of X1, ..., Xn, i.e., Yn = max(X1,.., Xn). %3D (a) Show that both 6, and ô2 are unbiased estimators of 0. (b) Find the efficiency of 61 relative to 02.
Transcribed Image Text:Let X1,., Xn denote a random sample from the uniform distribution on the interval (0,0 + 1). Let 1 n n, = X – and Ô2 = Yn - 2' n+1' where Y, is the nth order statistic of X1, ..., Xn, i.e., Yn = max(X1,.., Xn). %3D (a) Show that both 6, and ô2 are unbiased estimators of 0. (b) Find the efficiency of 61 relative to 02.
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