Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following probability density function: f(x; 0) = 1 V2πθ 0, e , if -∞0 < 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. (iv) Find the Fisher information in this sample of size n about the parameter 0.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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b)
Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following
probability density function:
1
f(x;0)=√√20
0,
x²
e 20
if -∞0 < x < 00
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 8.
Transcribed Image Text:b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following probability density function: 1 f(x;0)=√√20 0, x² e 20 if -∞0 < x < 00 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 8.
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