ECI 114
Fall
2008
Name
Solution
Midterm 1 (100 points)
Monday, October 20, 2008
Show your work. It’s not necessary to give a final numerical answer unless specifically asked, but you need to
provide all the information necessary to compute the final answer. Please circle or otherwise highlight your an-
swer. Turn in your “crib sheet” with your exam. Put your name on the back of the last page.
GOOD LUCK!
1.
For each of the following statements, circle the letter “T” if it is true, and “F” if it is false.
(3 * 8 =24 pts)
T
F
a.
Among measures of central tendency, the median and mode are actual data
values in the data set.
Answer:
If the number of observations is even, the median is halfway between the two central values. So
in that case the median would not be an actual value in the data set.
T
F
b.
If A and B form a partition and B and C are collectively exhaustive, then
A
∩
C=A.
Answer
: Ah
B=S and A
∩
B=
φ
; Bh
C=S. It’s easy to find
A
C
⊇
, so A
C=A.
T
F
c.
If a true-false exam contains 10 questions, there are 20 different possible sets of
answers.
Answer:
For each question, there are 2 ways to answer; so for the 10 questions, there are 2
10
ways
to answer all the questions.
T
F
d.
Pr[A]=
]
,
,
|
Pr[
*
]
,
|
Pr[
*
]
|
Pr[
]
Pr[
C
B
A
D
C
A
B
A
C
D
C
B
A
.
Answer:
Using the chain rule, we get:
A
B
C
1
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]
,
,
|
Pr[
*
]
,
|
Pr[
*
]
|
Pr[
*
]
Pr[
]
Pr[
C
B
A
D
C
A
B
A
C
A
D
C
B
A
=
T
F
e.
0! = 0.
Answer:
0! = 1.
T
F
f.
For any set of N objects, taking n at a time, the number of combinations is never
less than the number of permutations.
Answer:
!
n
P
n
N
n
N
=
.
Since n!
≥
1,
n
N
n
N
P
!
n
P
n
N
≤
=
.
T
F
g.
If A and B are independent, Pr[
B
A C
]=Pr[A]+Pr[B].
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- Winter '08
- Mocktarian
- Conditional Probability, Probability, Probability theory
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