1
IOE 265 Fall 2007 1
st
Exam (80 minute exam)
October 8, 2007
Part I. Multiple choice questions
BCDBD
Part II.
True/False Problems
TFTFT
Part III. Fill in Blanks
0.205; 0.40; 0.951; k=12/25;
()
4
4
0
.
4
0
.
6
xx
PX x
x
−
⎛⎞
==
⎜⎟
⎝⎠
or b(x; 4, 0.4) or
binomial (n=4; p=0.4)
Part IV. Short Questions
1. A customer visiting the suit department of a certain store will purchase:
•
A suit with probability 0.22
•
A shirt with probability 0.30
•
A tie with probability 0.28
•
Both a suit and a shirt with probability 0.11
•
Both a suit and a tie with probability 0.14
•
Both a shirt and a tie with probability 0.10
•
All three items with probability 0.06
What is the probability that a customer purchase none of the items?
Solution:
A: suit
B: shirt
C: tie
[]
(' ' '
)1 (
)
1
(
)
(
)
(
)(
)
1
0.22 0.30 0.28 0.11 0.14 0.10 0.06
1 0.51
0.49
PA B C
PAPBPC PA B PA C PB C
=−
−
−
−
+
=
−
++−−−+
=
∩∩
∪∪
∩∩∩∩
∩
2. Assume X is a continuous random variable with the following density function:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
3
1
00
45
0
1
1
x
x
X
xx
ex
−
<
⎧
⎪
=≤
<
⎨
⎪
≥
⎩
a.
Obtain and sketch the cumulative distribution function.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '07
 Jin
 Normal Distribution, Probability, Probability theory

Click to edit the document details