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APPM 4/5570
Solutions to Problems from Sections 3.4 and 3.5
46.
b
(
x
;
n, p
) is notation for
P
(
X
=
x
) when
X
∼
bin
(
n, p
)
P
(
X
=
x
) =
n
x
!
p
x
(1

p
)
n

x
B
(
x
;
n, p
) is notation for
P
(
X
≤
x
) which involves summing up appropriate
values of
b
(
x
;
n, p
).
a.
P
(
X
= 3) =
8
3
!
(0
.
35)
3
(1

0
.
35)
8

3
≈
0
.
2786
b.
P
(
X
= 5) =
8
5
!
(0
.
6)
5
(1

0
.
6)
8

5
≈
0
.
2787
c.
P
(3
≤
X
≤
5)
=
P
(
X
= 3) +
P
(
X
= 4) +
P
(
X
= 5)
=
7
3
!
(0
.
6)
3
(1

0
.
6)
7

3
+
7
4
!
(0
.
6)
4
(1

0
.
6)
7

4
+
7
5
!
(0
.
6)
5
(1

0
.
6)
7

5
≈
0
.
7451
d.
P
(1
≤
X
)
=
P
(
X
≥
1) = 1

P
(
X
= 0)
=
1

9
0
!
(0
.
1)
0
(1

0
.
1)
9

0
=
1

(0
.
9)
9
≈
0
.
6126
49. For a randomly selected goblet, let a “success” be that it is “a second”. The the
probability of success when we look at any one goblet is
p
= 0
.
10. Let
X
be the
number of “seconds” in a random sample of 6 goblets. Then
X
∼
bin
(6
,
0
.
10)
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View Full Document a.
P
(
X
= 1) =
6
1
!
(0
.
10)
1
(0
.
90)
6

1
= 0
.
354294
b.
P
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This note was uploaded on 01/23/2011 for the course APPM 5440 at Colorado.
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