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) QUE TION f) f(x; 0) = {0, g) ((0+1)xº, if 0

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Question
Number F...G
Painter
11
Arial
-12
BIU abc
Y
x
- abc X, X
1977 WORDS
Type here to search
x² AA
A A Aa.
Aa
Font
a)
e o ge
QUE TION
d)
G
f)
ESENT
Let X1, X2, X3, Xn denote a random sample of size n from the population distributed with the
following probability density function:
9)
ENGLISH (SOUTH AFRICA)
==
What is the parameter space of o?
b) Find the maximum likelihood estimator (MLE) of o
Paragraph
Г
What is the MLE of g(0) = ?
1+0
Suppose that is a uniform minimum variance unbiased estimator of e. Show that the variance
of 0, Var(0) = (0+1)²
21
e) Use part d) of question 2 to show that is a consistent estimator of
AaBbCc AaBbCc AaBbC AaBbCcL AaB AaBbcct AaBbCcD AaBbCcD
T Normal 1 No Spac... Heading 1 Heading 2 Title
Subtitle
Subtle Em... Emphasis
O
O 1
f(x; 0) = {(0+1)xº, if 0<x<1
elsewhere
Show that , In (X) is a sufficient estimator of e. [Hint: Use one-parameter regular
exponential family]
Estimate using the method of moment estimator
0
(QUESTION 3
Styles
a
[28]
w
20°C
EM
ER
40 ENG
Sig
09:15
2022/11/08
Find
Replace
Select
F Editing
+ 100
Transcribed Image Text:Painter 11 Arial -12 BIU abc Y x - abc X, X 1977 WORDS Type here to search x² AA A A Aa. Aa Font a) e o ge QUE TION d) G f) ESENT Let X1, X2, X3, Xn denote a random sample of size n from the population distributed with the following probability density function: 9) ENGLISH (SOUTH AFRICA) == What is the parameter space of o? b) Find the maximum likelihood estimator (MLE) of o Paragraph Г What is the MLE of g(0) = ? 1+0 Suppose that is a uniform minimum variance unbiased estimator of e. Show that the variance of 0, Var(0) = (0+1)² 21 e) Use part d) of question 2 to show that is a consistent estimator of AaBbCc AaBbCc AaBbC AaBbCcL AaB AaBbcct AaBbCcD AaBbCcD T Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle Subtle Em... Emphasis O O 1 f(x; 0) = {(0+1)xº, if 0<x<1 elsewhere Show that , In (X) is a sufficient estimator of e. [Hint: Use one-parameter regular exponential family] Estimate using the method of moment estimator 0 (QUESTION 3 Styles a [28] w 20°C EM ER 40 ENG Sig 09:15 2022/11/08 Find Replace Select F Editing + 100
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