8. Let the n-vector y be a vector of mutually independent realizations from the uniform distribution on the interval (a, ẞ), that is, yi ~ U(a, B), i = 1, 2, ..., n. (a) What is the likelihood function of a and B (b) Find the MLEs â and B. (c) Suppose that the true values of the parameters are ao = 0 and B0 = 1. Show that the CDF of â is F(a) = Pr[â ≤ a] = 1 − (1 − a)". Use this result to show that n(â ao) is asymptotically exponentially distributed.
8. Let the n-vector y be a vector of mutually independent realizations from the uniform distribution on the interval (a, ẞ), that is, yi ~ U(a, B), i = 1, 2, ..., n. (a) What is the likelihood function of a and B (b) Find the MLEs â and B. (c) Suppose that the true values of the parameters are ao = 0 and B0 = 1. Show that the CDF of â is F(a) = Pr[â ≤ a] = 1 − (1 − a)". Use this result to show that n(â ao) is asymptotically exponentially distributed.
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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Hanny
![8. Let the n-vector y be a vector of mutually independent realizations from the uniform
distribution on the interval (a, ẞ), that is, yi ~ U(a, B), i = 1, 2, ..., n.
(a) What is the likelihood function of a and B
(b) Find the MLEs â and B.
(c) Suppose that the true values of the parameters are ao = 0 and B0 = 1. Show that
the CDF of â is F(a) = Pr[â ≤ a] = 1 − (1 − a)". Use this result to show that
n(â ao) is asymptotically exponentially distributed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6332589-6554-4f06-a125-958606746408%2Fb09c6101-cb66-47e8-89bd-23a9bfc0819d%2Fzvvrz4h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. Let the n-vector y be a vector of mutually independent realizations from the uniform
distribution on the interval (a, ẞ), that is, yi ~ U(a, B), i = 1, 2, ..., n.
(a) What is the likelihood function of a and B
(b) Find the MLEs â and B.
(c) Suppose that the true values of the parameters are ao = 0 and B0 = 1. Show that
the CDF of â is F(a) = Pr[â ≤ a] = 1 − (1 − a)". Use this result to show that
n(â ao) is asymptotically exponentially distributed.
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