Say you have an iid random sample of size n from the following density: Jaß(1+ Bx)-a-1 f(x) = if x > 0 otherwise, where a > 0 and B > 0. For this question, assume that ß is a known, fixed value and therefore does not need to be estimated. (a) Find E[X] (Note that it only exists when a > > 1). (b) estimator of a? Justify your answer. Find the method of moments estimator for a. Is this a consistent (c) Find the maximum likelihood estimator of a. (d) likelihood estimator of . Derive a large-sample 95% confidence interval for the maximum
Say you have an iid random sample of size n from the following density: Jaß(1+ Bx)-a-1 f(x) = if x > 0 otherwise, where a > 0 and B > 0. For this question, assume that ß is a known, fixed value and therefore does not need to be estimated. (a) Find E[X] (Note that it only exists when a > > 1). (b) estimator of a? Justify your answer. Find the method of moments estimator for a. Is this a consistent (c) Find the maximum likelihood estimator of a. (d) likelihood estimator of . Derive a large-sample 95% confidence interval for the maximum
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Say you have an iid random sample of size n from the following density:
JaßB(1+ Ba)-a-1
if x > 0
f (x) =
otherwise,
where a > 0 and B > 0. For this question, assume that B is a known, fixed value
and therefore does not need to be estimated.
(a)
Find E[X] (Note that it only exists when a > 1).
(ъ)
estimator of a? Justify your answer.
Find the method of moments estimator for a. Is this a consistent
(c)
Find the maximum likelihood estimator of a.
(d)
likelihood estimator of a.
Derive a large-sample 95% confidence interval for the maximum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b42026-ffd5-4641-b1f2-8aa8b085cbc7%2F34900445-8f14-4f3e-9cc1-2f07ab55f029%2F0g77raf_processed.png&w=3840&q=75)
Transcribed Image Text:Say you have an iid random sample of size n from the following density:
JaßB(1+ Ba)-a-1
if x > 0
f (x) =
otherwise,
where a > 0 and B > 0. For this question, assume that B is a known, fixed value
and therefore does not need to be estimated.
(a)
Find E[X] (Note that it only exists when a > 1).
(ъ)
estimator of a? Justify your answer.
Find the method of moments estimator for a. Is this a consistent
(c)
Find the maximum likelihood estimator of a.
(d)
likelihood estimator of a.
Derive a large-sample 95% confidence interval for the maximum
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