, , , . ( ). , .
, , , (f (x) = const a ≤ x ≤ b, f (x) = 0 x < a, x > b.
, f (x) , .
:
.
, (. 6), () , 4 . 1 , 2 .. i
Xi | ||
pi | q | p |
, (i) = p.
: D (Xi) = 0²· q + 1²· p p ² = p p ² = p (1 p), 4
. . . . .
, - ( , - ). , , . , .
.
, , - , . .
.
p( | X M (X)| < ε) ≥ D (X) / ε². (13.1)
.
1 | 2 | |||
1 | 2 |
| X M (X)| < ε | X M (X)| ≥ ε , (| X M (X)| < ε) + + (| X M (X)| ≥ ε) = 1, , (| X M (X)| < ε) = 1 - (| X M (X)| ≥ ε). (| X M (X)| ≥ ε).
|
|
D (X) = (x 1 M (X))² p 1 + (x 2 M (X))² p 2 + + (xn M (X))² pn. , | X M (X)| < ε. , . , k .
D (X) ≥ (xk+ 1 M (X))² pk+ 1 + (xk+ 2 M (X))² pk +2 + + (xn M (X))² pn ≥ ε² (pk+ 1 + pk+ 2 + + pn).
, pk+ 1 + pk+ 2 + + pn , | X M (X)| ≥ ε, , . , D (X) ≥ ε² (| X M (X)| ≥ ε), (| X M (X)| ≥ ε) ≤ D (X) / ε². p( | X M (X)| < ε) ≥ D (X) / ε², - .