Теория вероятностей. Барышева В.К - 84 стр.

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H n = 30000, p = 0.0001.
n p
P
n
(k) =
λ
k
e
−λ
k!
λ : λ = np = 30000 · 0.0001 =
3 = M[X]
P
30000
(3) =
3
3
e
−3
3!
= 0.224042, k = 3.
P
30000
(0) =
3
0
e
−3
0!
= 0.049787, k = 0.
P
30000
(x > 10) = 1 −
9
P
k=0
3
k
e
−3
k!
=
= 1 −
3
0
e
−3
0!
+
3
1
e
−3
1!
+
3
2
e
−3
2!
+
3
3
e
−3
3!
+
+
3
4
e
−3
4!
+
3
5
e
−3
5!
+
3
6
e
−3
6!
+
3
7
e
−3
7!
+
3
8
e
−3
8!
+
3
9
e
−3
9!
=
= 1 −(0.049787 + 0.149361 + 0.224042+
+ 0.224042 + 0.168031 + 0.100819 + 0.050409 + 0.021604+
+ 0.008102 + 0.002701) = 1 − 0.998898 = 0.001102.
N
X
H X
x
1
= 0, x
2
= 1, x
3
= 2, x
4
= 3, x
5
= 4, x
6
= 5.
p = 5/100 = 0.05.
x
1
= 0 P
5
(0) = C
0
5
· 0.05
0
· 0.95
5
= 0.7737809
x
2
= 1 P
5
(1) = C
1
5
· 0.05
1
· 0.95
4
= 0.2036267
x
3
= 2 P
5
(2) = C
2
5
· 0.05
2
· 0.95
3
= 0.02143433
x
4
= 3 P
5
(3) = C
3
5
· 0.05
3
· 0.95
2
= 0.0011281
x
5
= 4 P
5
(4) = C
4
5
· 0.05
4
· 0.95
1
= 0.0000297
x
6
= 5 P
5
(5) = C
5
5
· 0.05
5
· 0.95
0
= 0.0000003

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