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b. For n ≥ 2, let X₁, X2,..., Xn be i.i.d. samples from the the uniform distribution U(0,0 + 1) where is some real number. Let X(1) ≤X(2) ≤ ≤ X(n) 12- be the order statistics of the sample. [i.] Show that (X(1), X(n)) is a sufficient statistic for 0. [ii.] Find an and b(0) such that an (b(0) — X(n)) → W in distribution, where W has an exponential distribution with density f(w) = e, for w> 0 and 0 elsewhere.

b. For n ≥ 2, let X₁, X2,..., Xn be i.i.d. samples from the the uniform distribution U(0,0 + 1) where is some real number. Let X(1) ≤X(2) ≤ ≤ X(n) 12- be the order statistics of the sample. [i.] Show that (X(1), X(n)) is a sufficient statistic for 0. [ii.] Find an and b(0) such that an (b(0) — X(n)) → W in distribution, where W has an exponential distribution with density f(w) = e, for w> 0 and 0 elsewhere.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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b. For n ≥ 2, let X1, X2,..., Xn be i.i.d. samples from the the uniform distribution U(0,0 + 1) where is some real number. Let X(1) ≤X(2) ≤ ≤ X(n) be the order statistics of the sample. Inmizolgd an →>> [i.] Show that (X(1), X(n)) is a sufficient statistic for 0. [ii.] Find and b(0) such that an (b(0)-X(n)) W in distribution, where W has an exponential distribution with density f(w) = e-", for w> 0 and 0 elsewhere. lo todos
Transcribed Image Text:b. For n ≥ 2, let X1, X2,..., Xn be i.i.d. samples from the the uniform distribution U(0,0 + 1) where is some real number. Let X(1) ≤X(2) ≤ ≤ X(n) be the order statistics of the sample. Inmizolgd an →>> [i.] Show that (X(1), X(n)) is a sufficient statistic for 0. [ii.] Find and b(0) such that an (b(0)-X(n)) W in distribution, where W has an exponential distribution with density f(w) = e-", for w> 0 and 0 elsewhere. lo todos
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