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1
STAT 330 Assignment 1 Solutions
Question 1.
S=
123
124
125
213
214
215
13
14
15
23
24
25
3
4
5
Question 2:
Let
W
denote the even that the first ball is white and
B
denote the event that the
second ball is black.
Then
)
(
)

(
)
(
)

(
)
(
)

(
)

(
W
P
W
B
P
W
P
W
B
P
W
P
W
B
P
B
W
P
+
=
=
( )
( )
( )
m
n
m
k
m
n
k
m
m
n
n
k
m
n
m
m
n
n
k
m
n
m
+
+
+
+
+
+
+
+
+
+
+
=
k
m
n
n
+
+
Question 3:
We are given that
)
(
)
(
B
P
AB
P
=
and must show that this implies that
)
(
)
(
c
c
c
A
P
A
B
P
=
.
One way is as follows
)
(
)
(
)
(
1
)
(
1
)
)
((
)
(
AB
P
B
P
A
P
B
A
P
B
A
P
A
B
P
c
c
c
+
−
−
=
∪
−
=
∪
=
)
(
)
(
1
c
A
P
A
P
=
−
=
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Question 4:
a.
Since
1
)
(
0
=
∑
∞
=
i
i
p
, we have that
1
!
0
=
∑
∞
=
i
i
i
c
θ
implying, because
∑
∞
=
=
0
!
i
i
x
i
x
e
, that
1
=
ce
or
.
−
=
e
c
b.
−
−
=
=
=
e
e
X
P
!
0
/
)
0
(
0
c.
.
2
1
)
2
(
)
1
(
)
0
(
1
)
2
(
1
)
2
(
2
−
−
−
−
−
−
=
=
−
=
−
=
−
=
≤
−
=
>
e
e
e
X
P
X
P
X
P
X
P
X
P
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This note was uploaded on 07/12/2010 for the course STAT 330 taught by Professor Paulasmith during the Winter '08 term at Waterloo.
 Winter '08
 PAULASMITH

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