IOE 265 W2008
Practice Exam I  Solutions
1 of 7
Part I. Multiple Choice (10 questions, 3 points each, 30 points total)
1.
Which of the following statements is (are) true about a Poisson probability
distribution with parameter
λ
?
a.
The mean of the distribution is
λ
b.
The standard deviation of the distribution is
λ
c.
The parameter
λ
must be between 0 and 1
d.
All of the above
2.
Which of the following is not a condition of a binomial experiment?
a.
There is a sequence of n identical trials.
b.
Each trial results in at least two outcomes.
c.
The trials are independent of each other.
d.
The probability of success
p
is constant from one trial to another.
3.
If
X
is a continuous random variable defined on the interval [
A
,
B
], and the probability
density function of
X
is
(; , )
fxAB
=
1/(
)
0
otherwise
BA
AxB
−
≤≤
⎧
⎨
⎩
then
X
is said to have:
a.
Geometric Distribution
b.
Uniform Distribution
c.
Hypergeometric Distribution
d.
Normal Distribution
4.
Let
k
A
A
A
K
,
,
2
1
be mutually exclusive and exhaustive events.
Then for any other
event
B
,
()
()()
( ) ( )
k
k
A
P
A
B
P
A
P
A
B
P
B
P
+
+
=
K
1
1
is known as:
a.
The multiplication rule
b.
Bayes Theorem
c.
The law of total probability
d.
The additive rule
5.
Let
12
and
A
A
be mutually exclusive and exhaustive events, with
P
1
A
= 0.10 and
P
2
A
= 0.25.
Let
B
be any event such that
P
1
(/ )
= 0.50 and
P
2
= 0.80, then
the
P
1
(/)
A
B
is:
a.
0.05
b.
0.2*
c.
0.25
d.
None of the above
*Using Bayes Theorem:
( )
() ()
2
0
8
0
25
0
5
0
1
0
5
0
1
0
2
2
1
1
1
1
1
.
)
.
)(
.
(
)
.
)(
.
(
)
.
)(
.
(
A
B
P
A
P
A
B
P
A
P
A
B
P
A
P
B
A
P
=
+
=
+
=
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Practice Exam I  Solutions
2 of 7
6.
If two events A and B are independent then:
a.
P(A)= P(AB)
b.
P(A
∩
B)= P(A)×P(B)
c.
P(A)<=1
d.
both (a) and (b)
7.
The probability mass function of a discrete random variable X is defined as
p(x) = x/10 for x = 0,1,2,3,4.
The value of the cumulative distribution function F(x)
at x= 3 is
a.
0.10
b.
0.30
c.
0.60
d.
0.90
x0 1
2
34
f(x)
0
0.1
0.2
0.3
0.4
F(x)
0
0.1
0.3
0.6
1
8.
Which of the following statements is not an example of a discrete random variable?
a.
The number of female respondents to a questionnaire about gender differences
b.
The number of defects per square meter of a cotton fabric
c.
The average sales a salesperson makes per year
d.
The number of schoolage children with a single parent
9.
Which of the following statements is always true?
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 Winter '07
 Jin
 Normal Distribution, Probability theory, A. B, W2008 Practice Exam

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