=) Let X: {x, , X2,... Xn 3 be a rindom sample grom a mormal diseribution with mean M Gnd variance o that i (X; - «)* is i. I u is Enown and o is untnown , show o?. Show all a sufgicient Statistic the working steps. gor I1. I u and oé are both untnuwn show that X C the sample mean) and 5 C the sample veriance) are -) Now, let X: { X, , X2, jointly sufgicient gur u ünd o?. C. Ccod .... distci L. ti
=) Let X: {x, , X2,... Xn 3 be a rindom sample grom a mormal diseribution with mean M Gnd variance o that i (X; - «)* is i. I u is Enown and o is untnown , show o?. Show all a sufgicient Statistic the working steps. gor I1. I u and oé are both untnuwn show that X C the sample mean) and 5 C the sample veriance) are -) Now, let X: { X, , X2, jointly sufgicient gur u ünd o?. C. Ccod .... distci L. ti
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![normal distribution with mean
1.ca) Let X: { X,, X2,... Xn} be a rindom sample grom a
e and variance o
in
i. I u is tnown and o is untnown, show that i (X; - «)
gur o. Show all the working steps.
Statistic
2
". I u and o?
are both untnown
show that X ( the sample mean) and S
( the sample veriance) are
X2,
distri bution. Consider the
jointly sug gicient
X25} be a random Sample from a NCu, 1)
gur u urd o?
u cind o?
(b) Now, let X:} X,
from a NCu,1)
...
te st
of :
Ho : M:4.0
VS. Hi: M: 3.0
that
regects
Ho
iç the sam ple mean is less thon
3.5
i. Calculate the size
the
test , your answer in
of
C the standord nor mal cumulative distribution
ex pressing
of $
terms
functi on)
ii. Colculate the power of
the test, ex pressing your Gnsuer
ini Caleulate the probability of
ype i
error
expressing your Gnswer
in ter ms of D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04d9642d-4ab3-4092-a0db-f80a75f414f4%2F6aec7b74-a35b-450f-9850-660b7ce89b95%2F4bqaq68_processed.jpeg&w=3840&q=75)
Transcribed Image Text:normal distribution with mean
1.ca) Let X: { X,, X2,... Xn} be a rindom sample grom a
e and variance o
in
i. I u is tnown and o is untnown, show that i (X; - «)
gur o. Show all the working steps.
Statistic
2
". I u and o?
are both untnown
show that X ( the sample mean) and S
( the sample veriance) are
X2,
distri bution. Consider the
jointly sug gicient
X25} be a random Sample from a NCu, 1)
gur u urd o?
u cind o?
(b) Now, let X:} X,
from a NCu,1)
...
te st
of :
Ho : M:4.0
VS. Hi: M: 3.0
that
regects
Ho
iç the sam ple mean is less thon
3.5
i. Calculate the size
the
test , your answer in
of
C the standord nor mal cumulative distribution
ex pressing
of $
terms
functi on)
ii. Colculate the power of
the test, ex pressing your Gnsuer
ini Caleulate the probability of
ype i
error
expressing your Gnswer
in ter ms of D
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