Let X1, X2,..., X₂ be a random sample from a uniform distribution on the interval [0, 0], so that 0 ≤ x ≤ 0 f(x) = Ꮎ 0 otherwise Then if Y = max (X), it can be shown that the rv U = Y/O has density function [nun-1 0 ≤ u≤1 otherwise fu(u) = 0 a. Use fu(u) to verify that Y (a/2)1 ≤ (1 - a/2)) = 1 = 1-a and use this to derive a 100(1 - α)% CI for 0. b. Verify that P(a¹/n ≤ Y/0 ≤ 1) = 1 - α, and derive a 100(1 − a)% CI for 0 based on this probability statement. c. Which of the two intervals derived previously is shorter? If my waiting time for a morning bus is uniformly distributed and observed waiting times are x₁ = 4.2, x₂ = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4, derive a 95% CI for 0 by using the shorter of the two intervals.
Let X1, X2,..., X₂ be a random sample from a uniform distribution on the interval [0, 0], so that 0 ≤ x ≤ 0 f(x) = Ꮎ 0 otherwise Then if Y = max (X), it can be shown that the rv U = Y/O has density function [nun-1 0 ≤ u≤1 otherwise fu(u) = 0 a. Use fu(u) to verify that Y (a/2)1 ≤ (1 - a/2)) = 1 = 1-a and use this to derive a 100(1 - α)% CI for 0. b. Verify that P(a¹/n ≤ Y/0 ≤ 1) = 1 - α, and derive a 100(1 − a)% CI for 0 based on this probability statement. c. Which of the two intervals derived previously is shorter? If my waiting time for a morning bus is uniformly distributed and observed waiting times are x₁ = 4.2, x₂ = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4, derive a 95% CI for 0 by using the shorter of the two intervals.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let X1, X2,..., X₂ be a random sample from a uniform
distribution on the interval [0, 0], so that
0 ≤ x ≤ 0
f(x)
=
Ꮎ
0 otherwise
Then if Y = max (X), it can be shown that the rv
U = Y/O has density function
[nun-1 0 ≤ u≤1
otherwise
fu(u)
=
0
a.
Use fu(u) to verify that
Y
(a/2)1
≤ (1 - a/2)) = 1
= 1-a
and use this to derive a 100(1 - α)% CI for 0.
b. Verify that P(a¹/n ≤ Y/0 ≤ 1) = 1 - α, and derive
a 100(1 − a)% CI for 0 based on this probability
statement.
c. Which of the two intervals derived previously is
shorter? If my waiting time for a morning bus is
uniformly distributed and observed waiting times are
x₁ = 4.2, x₂ = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4,
derive a 95% CI for 0 by using the shorter of the two
intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe60e14a8-856f-447c-ac90-795ae43e00b4%2F104ef8f9-027a-4c61-8f42-d477bc386c6b%2Fm4vrxn_processed.png&w=3840&q=75)
Transcribed Image Text:Let X1, X2,..., X₂ be a random sample from a uniform
distribution on the interval [0, 0], so that
0 ≤ x ≤ 0
f(x)
=
Ꮎ
0 otherwise
Then if Y = max (X), it can be shown that the rv
U = Y/O has density function
[nun-1 0 ≤ u≤1
otherwise
fu(u)
=
0
a.
Use fu(u) to verify that
Y
(a/2)1
≤ (1 - a/2)) = 1
= 1-a
and use this to derive a 100(1 - α)% CI for 0.
b. Verify that P(a¹/n ≤ Y/0 ≤ 1) = 1 - α, and derive
a 100(1 − a)% CI for 0 based on this probability
statement.
c. Which of the two intervals derived previously is
shorter? If my waiting time for a morning bus is
uniformly distributed and observed waiting times are
x₁ = 4.2, x₂ = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4,
derive a 95% CI for 0 by using the shorter of the two
intervals.
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