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e a random sample of size n from a population with a uniform distribution on the interval (0, 0). Let , ) and U = istribution function u< 0, - Osus1, u> 1. nction for Y(n) is G,(Y) = X ,0 sys 0, so the distribution function for U is given by = P(Y(n)) s Ou = G, )- " v ,0sy s1. ution of U does not depend on 0, U is a pivotal quantity. Find a 95% lower confidence bound for 0.

e a random sample of size n from a population with a uniform distribution on the interval (0, 0). Let , ) and U = istribution function u< 0, - Osus1, u> 1. nction for Y(n) is G,(Y) = X ,0 sys 0, so the distribution function for U is given by = P(Y(n)) s Ou = G, )- " v ,0sy s1. ution of U does not depend on 0, U is a pivotal quantity. Find a 95% lower confidence bound for 0.

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,, Y2, ..., Y, denote a random sample of size n from a population with a uniform distribution on the interval (0, 0). Let Y(n) = max(Y1, Y2, ..., Y, ) and U = (n). (a) Show that U has distribution function u < 0, Fulu) = {u", (1, Osus1, u > 1. The distribution function for Yn) is G,(y) = X ,0 sys 0, so the distribution function for U is given by Flu) = P(U s u) = P(Y(n) s Ou = G, )- u" V ,0 sy 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,, Y2, ..., Y, denote a random sample of size n from a population with a uniform distribution on the interval (0, 0). Let Y(n) = max(Y1, Y2, ..., Y, ) and U = (n). (a) Show that U has distribution function u < 0, Fulu) = {u", (1, Osus1, u > 1. The distribution function for Yn) is G,(y) = X ,0 sys 0, so the distribution function for U is given by Flu) = P(U s u) = P(Y(n) s Ou = G, )- u" V ,0 sy 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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