P [ D x < (x < x >) < D x ] = a (20)
P [(< x >D x) < x < (< x > + D x)] = a (21)
a , . (< x > D x ) (< x > + D x ) .
(21) , , a, (< x >+D x ) (< x >D x ). , , , , , , .
: , ( ) . , , . . - .
, , , , , , .
, , , ( s) . , D x , s. (. . 69).
0.9 0.95.
, , 0.999. .
, , - , , 0.68. (, , , ). . , .11, .
.11.
< x > = 1.27, s = 0.03. , , 1.26 < xi < 1.28?
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0.01, ( s) 0.01: 0.03 = 0.31. .11 , e = 0.3 0.24,
, 1/4 0.01. , 1.20 < i < 1.34. , s, e = 0.07: 0.03 2.3. .11 a e = 2.3, 0.97. , 97% .
: , 98% ? .11 , a = 0.98 e = 2.4, se = 0.03´2.4 0.077, 1.193 < x < 1.347 , , 1.19 < x < 1.35; x = 1.27 0.08 0.98.
, , : ( ) . s 0.68, (2s) 0.95, (3s) 0.997.
.11.
a , , , . , , , .
r, (3), ( n > 30) S r :
S = 1.25× r r = 0.8× S, (22)
, s r, S r. n S/ r , , , S/r > s/r. r r r = 0.95× r.
s, p r.
, s, , . r , , s. [8]).
, n , , (22). n , , ( ) .
, (18),
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r = 1S n |< x > xi |/[ n ×(n 1)]1/2. (23)
n , , .
4.
, - .
, , .
, , , , .
-, s , a , 1. :
P ( | x < x >| < s×a ) > 1 1/a2. (24)
, ,
P ( | x < x >| < s×a ) > 1 4/9a2. (25)
.3 , , .
3.
as | P | P | P. |
0.68 | |||
1.5 | 0.87 | 0.2 | 0.7 |
0.95 | 0.75 | 0.89 | |
0.997 | 0.89 | 0.95 |
, , . , , . , , , , , ( ), .
, , .
5.
Z ( ) X Y, . , SX 2, SY 2, SZ 2 X, Y Z ,
SZ 2 = SX 2 + SY 2, (26)
SZ = |(SX 2 + SY 2)1/2|. (27)
Z , , , ( ) ( ) .