2.2.1 . . .
, . . , .
. . 0, 1, 2, 3,
, , . , , - . .
. , , .
, , .
. ( 24) :
xi | x1 | x1 | x1 | xn-1 | xn | |
i | 1 | 2 | 3 | n-1 | n |
xi x, i .
.2.2
, .
, X = x, X < x, F(x) x:
F(x) = P(X < x). (2.26)
, 0 1 ( 25).
:
F(x) = ∑ P(X = x). (2.27)
2.3
(2.27) i, . -
2.4
, ( 2.4), ( = ). F() .
|
|
f(), :
f(x) = F΄(x). (2.28)
, .
2.5
, , , f(x). , ( 2.6).
2.6
, . . , , .
2.2.2 . ( ) . , .
: , , , .
, , , . .
, λ = const. .
(2.29)
2.7 (t)
2.8 f(t)
2.9 λ(t)
, .
. . . , (2.29) .
|
|
)
)
)
)
, , .. , . , .
, (2.30)
, σ , .. ( ) .
( ) 3σ .
t
, (2.31)
(z) = .
(z) z = (T0 t)/σ, (2.31)
. (2.32)
(z) , (-z) = - (z). z [7, 8, 9].
λ(t)
(2.33)
2.10 (t)
2.11 f(t)
2.12 λ(t)
, . , . t , . , , .
, . , , r, t. , , r,
(2.34)
(r) t;
, t( ).
, (2.34)
(2.35)
t , r ;
.
(2.35) r = 0 r = ∞ t/T.
. , r = 0, 1, 2, 3 .., (2.35) , , ..
|
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(2.36)
. , t, .. P(t) = . , r = 0. (2.36) , t ..
35 . r t/T.
2.13
. t = . 35 , (0) = 37%, (1) = 37%, (2) = 18%, (3) = 6% ..
35, . = 200 . t = 100 , t/T = 0,5. , 55%, 30%, 9%, 2%.
, , ..
= σ2(r). (2.37)
.
. .
,
(2.38)
b .
(2.39)
(2.38) (2.39) , , , a b.
b < 1 (2.39) , .
b = 1 .
(2.40)
(2.39) (2.40)
(2.41)
2.14 (t)
2.15 f(t)
2.16 λ(t)
( ) ()
= b; (2.42)
σ() = b, (2.43)
(2.44)
(2.45)
- -, [4, 5, 6].
v(t), ,
(2.46)
. b, . . (. (2.15))
|
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(2.47)
σ . [4,5,6] b, b b. (2.42) (2.43), σ. b .