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Statistics 400
Midterm Exam 2
April, 14th 2011, Thursday, 12:301:50pm
Name:
Net I.D.
Discussion Section (circle one):
BD1
BD2
BD3
BD5
1. Please
print
your name and Net ID number in the above space and circle the dis
cussion section number.
2. This is a closed book, closednotes examination. You should have a calculator and a
single twosided page of notes that you may refer to.
3. Please provide the answers in the space provided. If you do not have enough space,
please use the back of a nearby page or ask for additional blank paper. Make sure
you sign any loose pages.
4. In order to receive full credit for a problem, you should show all of your work and
explain your reasoning. Good work can receive substantial partial credit even if the
ﬁnal answer is incorrect.
5. In most cases the later parts of a question do not require the answers to earlier parts.
You should try all parts of a problem even if you get stuck on an early part.
Question
Points
Question 1 ( 20 points)
Question 2 ( 22 points)
Question 3 ( 19 points)
Question 4 ( 21 points)
Question 5 ( 12 points)
Question 6 ( 6 + 5
bonus
points)
Total ( 105 points)
1
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View Full Document 1.
[20 points]
Let
X
and
Y
have the joint p.d.f.
f
X,Y
(
x,y
) =
‰
2(
x
+
y
)
,
0
≤
x
≤
y
≤
1
0
,
elsewhere
(a)
[8 points]
Find the marginal p.d.f.’s of
f
1
(
x
).
f
1
(
x
) =
Z
1
x
2(
x
+
y
)d
y
= (2
xy
+
y
2
)

1
x
= 1 + 2
x

3
x
2
,
0
≤
x
≤
1
(b)
[12 points]
Compute
μ
x
and
σ
2
x
.
μ
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This note was uploaded on 09/11/2011 for the course STAT 400 taught by Professor Tba during the Spring '05 term at University of Illinois at Urbana–Champaign.
 Spring '05
 TBA
 Statistics, Probability

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