Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: e) g) of 0, Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² Var (8) = ! f(x; 0) = {(0 + 1)xº, 0, n if 0 < x < 1 elsewhere Use part d) of question 2 to show that is a consistent estimator of 0. Show that ₁ ln(X;) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family]. Estimate using the method of moment estimator.
Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: e) g) of 0, Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² Var (8) = ! f(x; 0) = {(0 + 1)xº, 0, n if 0 < x < 1 elsewhere Use part d) of question 2 to show that is a consistent estimator of 0. Show that ₁ ln(X;) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family]. Estimate using the method of moment estimator.
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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![Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the
following probability density function:
e)
g)
of Ô,
Suppose that Ô is a uniform minimum variance unbiased estimator of 0. Show that the variance
(0+1)²
Var (ê) = !
f(x; 0) = {(0 + 1)xº,
0,
n
if 0 < x < 1
elsewhere
Use part d) of question 2 to show that is a consistent estimator of 0.
Show that ₁ ln(X;) is a sufficient estimator of 0. [Hint: Use one-parameter regular
exponential family].
Estimate using the method of moment estimator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c17a710-26d7-4116-b1b9-95b1f447e8a0%2Fbcdb7057-f1a4-41af-9b6c-84ea1c51b1b7%2Fvvuz4h6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the
following probability density function:
e)
g)
of Ô,
Suppose that Ô is a uniform minimum variance unbiased estimator of 0. Show that the variance
(0+1)²
Var (ê) = !
f(x; 0) = {(0 + 1)xº,
0,
n
if 0 < x < 1
elsewhere
Use part d) of question 2 to show that is a consistent estimator of 0.
Show that ₁ ln(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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