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Stat312: Sample Midterm I.
Moo K. Chung
mchung@stat.wisc.edu
September 30, 2004
Answer all questions clearly and circle your ﬁnal an
swer. If you submit two contradicting computations and
answers, the grade will be the minimum of two. Correct
answers without valid computation or explanation will
not get full credit. If you used a wrong formula without
much explanation of what you are doing and ended up
submitting a wrong solution, you will get almost noth
ing.
1. Let
X
1
,
···
,X
n
be a random sample from a nor
mal distribution with mean
μ
and variance
σ
2
.
(a) What is
E
(
S
2
/σ
2
)
?
S
2
is the sample variance.
Explain your result (5 points).
(b) Among all estimators of the form
aX
1
+
bX
2
,
ﬁnd the minimum variance unbiased estimator of
2
μ
(10 points).
2. Consider the sample of fat content of 10 randomly
selected dogs: 25, 21, 22, 17, 29, 25, 16, 20, 19, 22.
Suppose that these are from a normal population.
(a) Find the sample standard deviation using two
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This homework help was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Fall '04 term at Wisconsin.
 Fall '04
 Chung
 Statistics

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