.
x M x, x D x = M (x - M x)2.
, D x = M (x - M x)2= M x 2 - M (x)2.
, . M x 2 >
, .
, .
:
- , D x 0;
- , D c =0;
- D (cx) = c 2 D (x);
- : D (x h) = D (x) + D (h).
51) , , , , , ..
F(x)=P(X<x)
.
:
1. [0;1]: 0 F(x) 1
2. F(x) - , .. F(x2) F(x1), x2>x1
1. , , (a,b), :
P(a X<b)=F(b)-F(a) (7)
9. :
, , (0;2): P(0<x<2)=F(2)-F(0)
: (0;2) , F(x)=x/4+1/4, F(2)-F(0)=(2/4+1/4)-(0/4+1/4)=1/2. , P(0<x<2)=1/2
2. , , .
3. (;b), : 1) F(x)=0 x a; 2) F(x)=1 x b.
:
, =0, =1 ( ). (;b), , . x a ; x b :
F(x), , , :
.
F(x) .
. , . . . pi .
|
|
. ( , ) f(x), :
.
54) . , [a,b],
, :
, , , .
. .
, :
. .