Section 3-8
3-97.
X has a hypergeometric distribution N=100, n=4, K=20
a.)
(
)(
)
(
)
4191
.
0
3921225
)
82160
(
20
)
1
(
100
4
80
3
20
1
=
=
=
=
X
P
b.)
, the sample size is only 4
0
)
6
(
=
=
X
P
c.)
(
)(
)
(
)
001236
.
0
3921225
)
1
(
4845
)
4
(
100
4
80
0
20
4
=
=
=
=
X
P
d.)
8
.
0
100
20
4
)
(
=
⎟
⎠
⎞
⎜
⎝
⎛
=
=
=
N
K
n
np
X
E
6206
.
0
99
96
)
8
.
0
)(
2
.
0
(
4
1
)
1
(
)
(
=
⎟
⎠
⎞
⎜
⎝
⎛
=
⎟
⎠
⎞
⎜
⎝
⎛
−
−
−
=
N
n
N
p
np
X
V
3-18

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3-98.
a)
( )(
)
(
)
4623
.
0
24
/
)
17
18
19
20
(
6
/
)
14
15
16
4
(
)
1
(
20
4
16
3
4
1
=
×
×
×
×
×
×
=
=
=
X
P
b)
( )(
)
(
)
00021
.
0
24
/
)
17
18
19
20
(
1
)
4
(
20
4
16
0
4
4
=
×
×
×
=
=
=
X
P
c)
( )(
)
(
)
( )(
)
(
)
( )(
)
(
)
9866
.
0
)
2
(
)
1
(
)
0
(
)
2
(
24
17
18
19
20
2
15
16
6
6
14
15
16
4
24
13
14
15
16
20
4
16
2
4
2
20
4
16
3
4
1
20
4
16
4
4
0
=
=
+
+
=
=
+
=
+
=
=
≤
⎟
⎠
⎞
⎜
⎝
⎛
×
×
×
⎟
⎠
⎞
⎜
⎝
⎛
×
×
+
×
×
×
+
×
×
×
X
P
X
P
X
P
X
P
d) E(X) = 4(4/20) = 0.8
V(X) = 4(0.2)(0.8)(16/19) = 0.539
3-99.
N=10, n=3 and K=4
0
1
2
3
0.0
0.1
0.2
0.3
0.4
0.5
x
P(x)
3-100.
(a) f(x) =
/
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
x
x
3
12
24
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
3
36
(b) μ=E(X) = np= 3*24/36=2
V(X)= np(1-p)(N-n)/(N-1) =2*(1-24/36)(36-3)/(36-1)=0.629
(c) P(X
≤
2) =1-P(X=3) =0.717
3-19