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8.43 Let Y₁, Y2,..., Y₁ denote a random sample of size n from a population with a uniform distri- bution on the interval (0, 0). Let Y(n) = max(Y₁, Y₂, ..., Y,) and U = (1/0)Y(n). a Show that U has distribution function 0, u < 0, 0≤u≤ 1, Fu (u) = u", 1, u > 1. b Because the distribution of U does not depend on 0, U is a pivotal quantity. Find a 95% lower confidence bound for 0.

8.43 Let Y₁, Y2,..., Y₁ denote a random sample of size n from a population with a uniform distri- bution on the interval (0, 0). Let Y(n) = max(Y₁, Y₂, ..., Y,) and U = (1/0)Y(n). a Show that U has distribution function 0, u < 0, 0≤u≤ 1, Fu (u) = u", 1, u > 1. b Because the distribution of U does not depend on 0, U is a pivotal quantity. Find a 95% lower confidence bound for 0.

Calculus For The Life Sciences
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.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 44CR
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8.43 Let Y₁, ₂, ..., Y₁ denote a random sample of size n from a population with a uniform distri- bution on the interval (0, 0). Let Y(n) = max(Y₁, Y₂, ..., Y₂) and U = (1/0)Y(n). a Show that U has distribution function 0, u < 0, 0≤u≤ 1, Fu (u) = u", 1, u > 1. 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:8.43 Let Y₁, ₂, ..., Y₁ denote a random sample of size n from a population with a uniform distri- bution on the interval (0, 0). Let Y(n) = max(Y₁, Y₂, ..., Y₂) and U = (1/0)Y(n). a Show that U has distribution function 0, u < 0, 0≤u≤ 1, Fu (u) = u", 1, u > 1. 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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