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Statistics 403 Problem Set 1
Due in lab on Friday, September 17th
1. Suppose we have the following probability distribution:
x
P
(
X
=
x
)
1
0.19
2
0.09
3
0.07
4
0.15
5
0.21
6
0.03
7
0.01
8
0.03
9
0.12
10
0.10
(a) What is the probability that
X
is odd?
Solution:
The probability that
X
is odd is
0
.
19 + 0
.
07 + 0
.
21 + 0
.
01 + 0
.
12 = 0
.
6
.
(b) What is the probability that
X
is evenly divisible by 3?
Solution:
X
is evenly divisible by 3 only if
X
equals 3, 6, or 9. Thus the probability is
0
.
07 + 0
.
03 + 0
.
12 = 0
.
22
.
(c) Are these two events independent? Why or why not?
Solution:
If the events are independent, the probabilities must satisfy the mul
tiplication rule. The value of
X
is both odd and evenly divisible by 3 only if
X
equals 3 or 9. This probability is 0
.
07+0
.
12 = 0
.
19, which is substantially greater
than the product 0
.
6
×
0
.
22 (where 0
.
22 is the probability that
X
is divisible by
3). Thus these two events are not independent (they are positively dependent).
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This note was uploaded on 02/06/2012 for the course STAT 403 taught by Professor Kerbyshedden during the Winter '12 term at University of MichiganDearborn.
 Winter '12
 KerbyShedden
 Statistics, Probability

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