Теория вероятностей. Барышева В.К - 59 стр.

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ТПУ | Томск

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X 500000 200000 100000 50000 10000 0
P
6
i=1
p
i
p 0.002 0.01 0.02 0.04 0.08 0.848 1
N
5
0.7.
F (x)
P (2 < x < 5).
H
Ω = {1, 01, 001, 0001, 00001, 00000},
{1} {0}
1, 2, 3, 4, 5.
p
1
= P (x
1
= 1) = P (1) = 0.7 p
2
= P (x
2
= 2) = P (01) = 0.3 · 0.7 = 0.21
p
3
= P (x
3
= 3) = P (001) = 0.3
2
· 0.7 = 0.063;
p
4
= P (x
4
= 4) = P (0001) = 0.3
3
· 0.7 = 0.0189;
p
5
= P (x
5
= 5) = P (00001 + 00000) = 0.3
4
· 0.7 + 0.3
5
= 0.0081.
X 1 2 3 4 5
P
5
i=1
P
i
P 0.7 0.21 0.063 0.0189 0.0081 1
F (x)
x 6 1, F (x) = P (X < x) = 0
1 < x 6 2, F (x) = P(X < x) = P
1
(X
1
= 1) = 0.7
2 < x 6 3, F (x) = P
1
(X = 1) + P
2
(x = 2) = 0.91
3 < x 6 4, F (x) = P
1
(x = 1) + P
2
(x = 2) + P
3
(x = 3) =
= 0.7 + 0.21 + 0.063 = 0.973
4 < x 6 5, F (x) = P
1
(x = 1) + P
2
(x = 2) + P
3
(x = 3) +
+P
4
(x = 4) = 0.973 + 0.0189 = 0.9919
x > 5, F (x) = 1

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