mx=M[x ] σ2x= D[x] = M[(X mx)2] = M[x2] . mx , , D[x] :
sx = (1.11)
. ( S) . mx .
. . a S. a* a*=a*(S) . , a* . ( ) a*, , , . .
1. . a* : M[a*] = a. , a* .
2. . , a* , .
3. . a* , . a* .
, , .
.
= , (1.12)
. X mx sx, (1.12) . , , X (..1.4, 1). . , (..1.1, 1) ,
(1.13)
(1.13) , , .
, . . (1.12), .
:
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= , (1.14)
, mi , i , zi . , , , , .
:
= , (1.15)
, .
:
= (1.16)
(1.14) (1.16), , , , , mx , i , zi.
, n, n /(n 1) (1.15) (1.16) , .
.
a a*(S) S. a* (.1.5), . , , . ,
a* ¹ a, , a* a. ? .
.1.5. .
. Ib = (a, b), b. Ib , b .
S, , a(S) b(S), () . b , Ib a. . 1.6. Ib a, Ib* - . , a .
b (, b = 0,999), a .
.1.6. a .
, .
mx . , , :
= , (1.17)
n , n, mx .
(1.18)
, j(t), .1.7 ( ..1.4, 1).
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.1.7. t.
b tb -,
b = 0(tb) 0(-tb) = 2 0(tb), (1.19)
- . (-tb, tb) .1.7. , , (1.19), b.
b = P(-tb < < tb) = P( tb < mx < + tb ) =
= P( tb < mx < + tb ). (1.20)
,
Ib = ( tb ; + tb ), (1.21)
(1.20) , mx Ib b. Ib b tb (1.19). tb, [3, 5]:
t0,9 = 1,645; t0,95 = 1,96; t0,99 = 2,58; t0,999 = 3,3.
(1.21) , s. . (1.15) :
Ib = ( tb ; + tb ). (1.22)
, , , :
Ib = ( tb ; + tb ). (1.23)
, (1.22) . , t j(t), n . s. . (1.23) , , , .
, b. , tb tb b = 0(tb) - 0(tb),
Ib = ( + tb ; + tb ),
b mx (.1.7.). , t0,9 = - 4 t0,9 = 1,282. 1,6 . (1.21) , .
, , [1, 5].