, . , , , , i, :
Fx=P[Xi<x]. (1.6)
fx, () , , F(- )=0, a F() = 1. [x1,x2] :
P[x1<Xi<x2]=FX(x2)-FX(x1)
() , :
(1.7)
1, 2,..., n fx . ,
,
P[x1<Xi<x2] = (1.8)
, . , , , fΔ 8.01172 . 1.1.
, . 1.1, . , , . . :
, (1.9)
:
( ) Xi,
, (1.10)
:
Dx , σ () i .
.1.1.
|
()
|
|
|
1
2
()
|
|
. 1.1 fx, (1.9) σx>σx>σx. , σx , . . , .
(1.9):
(Xi-mX)/σX=t, (1.11)
(1.8) [x1,x2]:
. (1.12)
F(t) . , σ (1.11) ( ) .
|
|
. 1.1. σx>σx>σx.
n<30 (1.9) :
(1.13)
:
-.
n>30 (1.13) (1.9) , , . (1.12)
P[x1<Xi<x2]=2F(t,n)-1,
:
F(t, n) , .
, . 11.00674. n>50 (λn), ( 2) ( 2). 3<n<50, (W).
, . 1.1, , . (. 1.2), (, , . .) , , . , , , () , , .
(.1.1). . :
(1.14)
:
, fx.
, α=1 (1.14) , α= 2 c (1.9), .
, , . , . . , (. 1.1), , (. 1.1) . , k-
|
|
(1.15)
k-
, (1.16)
:
X. , , .. i = 1/n.
(k=1), Xi. (1.15),
. (1.17)
(k=2) Xi. (1.16) (1.10),
. (1.18)
.
, , , , . (1.9) s=0 =0. m σ.
, , ( ) . , , , , . , , . , ^, , . , ( ) n . , . , , x = min.