Say you have an iid random sample of size n from the following density:Saß(1+ Bx)-a-1f(x) ={if x > 0otherwise,where a > 0 and B > 0. For this question, assume that B is a known, fixed valueand therefore does not need to be estimated.(a)Find E[X] (Note that it only exists when a > 1).Find the method of moments estimator for a. Is this a consistent(b)estimator of a? Justify your answer.(c)Find the maximum likelihood estimator of a.Derive a large-sample 95% confidence interval for the maximum(d)likelihood estimator of a.

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Answered: (a) Find E[X] (Note that it only exists…

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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Can you help me with this please! Thank you.
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(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 a. Derive a large-sample 95% confidence interval for the maximum