. , .
. , 30% . X - . , , 1- , 2- , . ., .
X : x 1 = 0, 2 = 1, x 3 = 2, x 4 = 3, 5 = 4, x 6 = 5, x 7, = 6, 8 = 7.
:
.
2.1
X | ||||||||
Pi | 0,0824 | 0,2472 | 0,3128 | 0,2263 | 0,0973 | 0,0250 | 0,0036 | 0,0002 |
, , .
. . , , - . M () D (X).
1. . . M () X
(2.2.1)
, . , N , X x 1 m 1 , 2 m 2 ,..., xk mk . ,
, () . .
.
1 . .
. , , , = 1. , ,
M (C) = C ∙1= C. (2.2.2)
2. , . .
M (CX) = CM (X) (2.2.3)
. : 1, 2, 3,..., Cxk, : 1 2, p 3 , p k.
3. .
. b - x 1, x 2, x 3,..., xk p l, 2, 3,..., pk.
|
|
ap 1 + ap 2 + + apk ≤ x 1 p 1 + x 2 p 2 + + xkpk ≤ bp 1 + bp 2 + + bpk,
,
p 1 + p 2 + + pk = 1,
A ≤ M (X) ≤ b (2.2.4)
.
4. , . .
M (X + Y)= M (X)+ M (Y) (2.2.5)
. , .
X Y , , .
5.
M (XY) = M (X)∙ M (Y) (2.2.6)
2. . . . . . , . , , . (), , i .
. D(X) X X
D (X) = M (X M (X))2 (2.2.7)
(X (X))2 . 2.2.
2.2
(xi M (X))2 | (x 1 M (X))2 | (x2 M (X))2 | (x3 M (X))2 | (xk M (X))2 | |
pi | p1 | p2 | p3 | pk |
D (X) = M (X M (X))2
D (X) = (2.2.8)
:
D (X) = M (X)2 (M (X))2 (2.2.9)
, .
.
1. X =1, D (X) = 0, . . .
.
D (X) = D (C) = M (C C)2 = M (0) = 0 (2.2.10)
2. , ,
D (CX) = C 2 D (X). (2.2.11)
3.
D (X Y) = D (X) + D (Y) (2.2.12)
. (2.2.9)
D (X Y) = M (X Y)2 - [ M (X Y)]2.
D (X Y) = M (X 2 2 XY+Y 2) [ M (X) M (Y)]2 =
= M (X 2) 2 M (X) M (Y) + M (Y 2) (M (X))2 2 M (X) M (Y) (M (Y))2 =
= M (X 2) (M (X))2 + M (Y 2) (M (Y))2 = D (X) + D (Y)
.
|
|
.
D(C+X) = D(X) (2.2.13)
D(X) . , . .
. σ() σ:
(2.2.14)