a) b) c) f(x; 0) = 0, What is the parameter space of 0? Find the maximum likelihood estimator (MLE) of 0. What is the MLE of g(0) ==? 1+8 elsewhere I

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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QUESTION 2
Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the
following probability density function:
a)
b)
c)
d)
e)
f)
g)
f(x; 0) = {0, +
((0+1)x, if 0<x< 1
elsewhere
What is the parameter space of 0?
Find the maximum likelihood estimator (MLE) of 0.
What is the MLE of g(0) ==?
Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance
of ê, Var(8) = (0+1)²
n
Use part d) of question 2 to show that is a consistent estimator of 0.
Show that
2 | Page
In(X) is a sufficient estimator of 0. [Hint: Use one-parameter regular
exponential family].
Estimate using the method of moment estimator.
Transcribed Image Text:QUESTION 2 Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: a) b) c) d) e) f) g) f(x; 0) = {0, + ((0+1)x, if 0<x< 1 elsewhere What is the parameter space of 0? Find the maximum likelihood estimator (MLE) of 0. What is the MLE of g(0) ==? Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance of ê, Var(8) = (0+1)² n Use part d) of question 2 to show that is a consistent estimator of 0. Show that 2 | Page In(X) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family]. Estimate using the method of moment estimator.
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