IE 230
Seat # ________
Name ___ < KEY > ___
Closed book and notes. 60 minutes.
Cover page and four pages of exam.
No calculator.
This exam covers event probabilities and the definition of random variables.
Chapter 2 of Montgomery and Runger, fourth edition.
A true/false question is true only if it is always true;
that is, if it ever is false, then it is false.
No need to simplify answers.
(1 point) Write your name neatly, on all five pages.
(1 point) Circle your family name.
Score ___________________________
Exam #1, February 8, 2011.
Schmeiser
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Name _______________________
Closed book and notes. 60 minutes.
1. True or false. (3 points each) Consider an experiment. Assume that events
A
and
B
and
random variable
X
are defined. Recall that
∅
denotes the empty set and
S
denotes the
sample space.
(a)
T
←
F
←
Every replication of the experiment results in one or more outcomes.
(b)
T
←
F
The random variable
X
assigns a real number to every outcome.
(c)
T
F
←
The random variable is said to "occur" whenever
X
=
x
.
(d)
T
F
←
P(
B
)
=
P(
A

B
) P(
A
)
+
P(
A
′

B
) P(
A
′
)
(e)
T
F
←
P(
A

B
′
)
=
1
−
P(
A

B
).
(f)
T
←
F
P(
B

A
) P(
A
)
=
P(
A

B
) P(
B
).
(g)
T
F
←
If
A
and
B
are mutually exclusive, then P(
A
∩
B
)
=
P(
A
) P(
B
).
(h)
T
←
F
The four events (
A
∩
B
), (
A
′
∩
B
′
), (
A
∩
B
′
), and (
A
′
∩
B
) partition
the sample space.
(i)
T
F
←
For every replication of the experiment, both
A
and
B
occurring is
impossible.
2. Consider the HIV/AIDS example. Recall that
T
ij
denotes the event of (not necessarily the
first) virus transmission on the
j
th contact with partner
i
. Let
n
i
denote the number of
contacts with partner
i
. Let
n
denote the number of partners.
(a) (6 points) Write the event that virus is transmitted from partner 2.
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