b) Let X₁, X₂, X3X be a random sample of n from population X distributed with the following probability density function: 1 = {√² + e 0, f(x;0)=√210 if -8 < x <∞0 otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased.

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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b)
Let X₁, X₂, X3,...X₁ be a random sample of n from population X distributed with the following
probability density function:
1 -20,
e
f(x;0)=√2n0
0,
if -∞0 < x < 00⁰
otherwise
(i) Find the parameter space of 0.
(ii) Find the maximum likelihood estimator of 0.
(iii) Check whether or not the estimator obtained in (ii) is unbiased.
(iv) Find the Fisher information in this sample of size n about the parameter 0.
Transcribed Image Text:b) Let X₁, X₂, X3,...X₁ be a random sample of n from population X distributed with the following probability density function: 1 -20, e f(x;0)=√2n0 0, if -∞0 < x < 00⁰ otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 0.
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