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Stat 5101 First Midterm Exam
October 14, 2009
Name
Student ID
The exam is closed book and closed notes. You may use one 8
1
2
×
11
sheet of paper with formulas, etc. You may also use the handout on “brand
name distributions”. Put all of your work on this test form (use the back
if necessary). Show your work or give an explanation of your answer. No
credit for numbers with no indication of where they came from.
The points for the questions total to 100. There are 6 pages and 5 prob
lems.
1. [20 pts.] Suppose
X
is a random variable having probability mass function
(PMF) given by
x
1
2
3
4
5
f
(
x
)
1
/
7
2
/
7
1
/
7
2
/
7
1
/
7
(a) Calculate
E
(
X
).
(b) Calculate var(
X
).
1
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View Full Document(c) Calculate Pr(
X >
3).
2. [20 pts.] Suppose
X
is a random variable having PMF given by
x
1
2
3
4
5
6
7
f
(
x
)
1
/
28
1
/
14
3
/
28
1
/
7
5
/
28
3
/
14
1
/
4
Find the PMF of the random variable
Y
= (
X

2)(
X

4)(
X

6).
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