4.1. .
, , , , .
, , .
, , . , ,... ..., , 4.1:
4.1
... | ||||
p1 | ... |
, ,..., ,, , . . , ,
(4.1)
( ) (. 4.1):
.4.1.
, - . . .
.
F (x), , , :
(4.2)
- , .
F (x) ;
F(x) , (. 4.2):
F(x)
p3
p2
p1
x1 x2 0 3 x j
.4.2.
( ) :
(4.3)
.
:
(4.4)
(4.4) , , .
() . :
1) ()=, =const
2) M (CX)=CM (X) (4.5)
3) M (X+Y)=M(X)+M(Y), Y.
|
|
4) M (XY)=M (X)M(Y), Y .
M(X)= D(X) () . (X- ), ..:
D(X)=M(X- )2= pi,
=(X); , .. .
:
(4.6)
:
1) D(C)=0, =onst
2) D(CX)=C2D(X), (CX)= çCç (X) (4.7)
3) D(X+Y) =D(X)+D(Y),
.
, D(X) .
4.3. .
Y- X - , , , , . , 4.2:
4.2
... | ||||
... |
, .. , - , , , , .
- , , , - ,
(4.8)
, :
(4.9)
.
- , , - , (4.8), , (4.9).
4.4. .
n , :
1. , .
- .
2. , p, . q.
3. n - . , n .
, n , , m ( ),
(4.10)
q=1-.
(4.10) .
, :
) m ,
) m ,
) m ,
) m - :
- n , ; = 0,1,2,..., m,...,n ( 4.3).
|
|
4.3
=m | ... | m | ... | n | |||
... | ... |
(4.10) , . , , :
M(X)=n (4.11)
D(X)=nq (4.12)
, , (4.10) :
(4.13)
m - n , ( n ).
(4.13) . m m=0,1,2,...,n, , (4.13), ( 4.4):
4.4
M | ... | m | ... | n | |||
Pn;m | ... | ... |
, , . , , , 10 , 100 , , .
, n , , n< 10.
, , , , ..
M(X)=D(X)=n×p= . (4.14)