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Let Y,, Y,, ..., Y, denote a random sample of size n from a population with a uniform distribution on the interval (0, 6). Let Y max(Y1- (a) Show that U has distribution function 0, u<0, F(u) = {u", osus1, (1, u > 1. The distribution function for Yn) is G,(y) = ,0 sys 0, so the distribution function for U is given by FU(u) = P(U s u) = P(Y(n) s ou = G ,0sy s1. %3D

Let Y,, Y,, ..., Y, denote a random sample of size n from a population with a uniform distribution on the interval (0, 6). Let Y max(Y1- (a) Show that U has distribution function 0, u<0, F(u) = {u", osus1, (1, u > 1. The distribution function for Yn) is G,(y) = ,0 sys 0, so the distribution function for U is given by FU(u) = P(U s u) = P(Y(n) s ou = G ,0sy s1. %3D

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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Let Y,, Y,, ..., Y, denote a random sample of size n from a population with a uniform distribution on the interval (0, 0). Let Y(2) = max(Y,, Y,, ..., Y, ) and U = (n) Y(n): (a) Show that U has distribution function (0, F(u) = {u", (1, u< 0, 0 sus1, u> 1. The distribution function for Yn) is G,(y) = ,0sys 0, so the distribution function for U is given by FUlu) = P(U s u) = P(Y(n)) s Bu = G, ,0sy s1. (b) Because the distribution of U does not depend on 0, U is a pivotal quantity. Find a 95% lower confidence bound for 0.
Transcribed Image Text:Let Y,, Y,, ..., Y, denote a random sample of size n from a population with a uniform distribution on the interval (0, 0). Let Y(2) = max(Y,, Y,, ..., Y, ) and U = (n) Y(n): (a) Show that U has distribution function (0, F(u) = {u", (1, u< 0, 0 sus1, u> 1. The distribution function for Yn) is G,(y) = ,0sys 0, so the distribution function for U is given by FUlu) = P(U s u) = P(Y(n)) s Bu = G, ,0sy s1. (b) Because the distribution of U does not depend on 0, U is a pivotal quantity. Find a 95% lower confidence bound for 0.
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