, - (, , ..). , , , , . ,
| |||||||||
|
|
| |||||||
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, . , ( ) . , .
.
10. , τ (. .) , 0 t . , : λ = λ(t).
. , , , . (, ) , .
20. , , , , .
. , , . , , , , ( , , ).
30. , , ∆ t . , , , .
. , , , .
( ), , .
|
|
, 10 30 , , .
, . , .. .
, : () n , ( λi, i = 1,2, , n), , λ, , .. .
0 t ,
(), τ.
1. λ (τ) , ..
( = m) = pm (τ) = ,
a = σ2 = λ t.
. 1(Δ t) ( ) Δ t.
2.
1(Δ t) ≈ λΔ t (Δ t → 0).
1 . 1 2, 1, , .
|
λ | ||
pm (τ) = , (m = 0, 1, 2, ) | ||
, τ | p0 (τ) = ( = 0) = . | |
, τ k (k =1,2,3) | (<k) = | |
, τ k (k =1,2,3) | (≥k) = 1- | |
, τ | (≥1) = 1- | |
1(Δ t) ≈ λΔ t (Δ t → 0) | ||
(τ) | ( (τ)) = = λ t | |
(τ) | D ( (τ)) = λ t | |
(τ) | σ( (τ)) = = |
. .
|
|
3. λ
1) F (t) = P (T < t)
F (t) = 1- , t ≥ 0.
2)
f (t) = , t ≥ 0.
3) ( )
() = σ() = .
4)
D () = .
, () .
, , , , , .
, 8.20 8.02 , , , , 8.29 , 8.20 8.29, , ( 8.02 8.29).
.
t - f (t). S , ,
P (t > T + S | t > S) = P (t > T).
.
4. .
10. N (t) , (0, t), , N (t), : (T, T + S) S.
20. , , , .
30. h > 0 , .. P (N (h) > 1) = 0.