b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the f probability density function: 1 f(x; 0)=√√2π0 0, x² e 20, if -∞o < x < 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.
b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the f probability density function: 1 f(x; 0)=√√2π0 0, x² e 20, if -∞o < x < 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.
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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(ii) Use the Central Limit Theorem to compute P(0.5 < X < 1.5), for n = 30.
(iii) Use the Chebychev inequality to find the value of k for P(0.5 < X < 1.5), if n = 30.
Let X₁, X₂, X3,...,Xn be a random sample of n from population X distributed with the f
probability density function:
1
f(x; 0)=√2π0
0,
x²
e 20
if -∞<x<∞
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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