10. , , .
, τ , τ, ; ; . , , 2.
, :
1) 7 ;
2) 7 ;
3) 7 ;
4) ;
5) ;
6) ;
7) .
. , .
, . .
, .
, .
, , .., , 1,2,3 . .
2 .
X (τ) , τ (), .
1) τ = 1 = 4 m = 7. 2 1
pm (τ) = , .. p 7(4) = ≈ 0,143.
2) 4 1
( < k) = , .. ( (4) < 7) = ≈ 0,321.
3) 5 1
( (4) ≥ 7) = 1 ( (4) < 7) = 1 0,321 = 0,679.
4) τ = 1 . p 0(1) , , 2 1.
p 0(τ) = , .. p 0(1) = ≈ 0,135.
5) τ = 2 . ( (2) ≥ 1) , , 6 1.
( (2) ≥ 1) = 1 - , .. ( (2) ≥ 1) = 1 - ≈ 0,981.
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6) , , 3 4.
F (t) = P (T < t) = 1 - , .. P (T < ) = F () = 1 ≈ 0,393.
7) , , 3 4.
P (T ≥ ) = 1 P (T < ) = 1 0,393 = 0,607. ►
11. , , , . . . 3- .
, :
1) 5 ;
2) 5 ;
3) 5 ;
4) ;
5) 1 ;
6) 3- ;
7) 3- .
. 3 λ. 8 .
p 5(16) ≈ 0,174;
( (16) < 5) ≈ 0,384;
( (16) ≥ 7) ≈ 0,616;
p 0(8) ≈ 0,069;
( (24) ≥ 1) ≈ 0,999;
P (T < 3) ≈ 0,632;
P (T ≥ 3) ≈ 0,368.►
12. , , . , , τ, , . , , , - .
.
, , : λ(t) = .
1) 6 ;
2) 6 ;
3) 5 ;
4) ;
5) ;
6) , ;
7) , .
. , .
.
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(t 0, τ) t 0 t 0 + τ, (t 0) , t 0.
:
1) τ = 1 = 4 , t 0 = 0, m = 6.
2 2 = ( (0; 4)) (0; 4)
= ( (0; 4)) = = = = 4,525.
3 2
6(0; 4) = ≈ 0,129.
2) τ = 1 = 4 , t 0 = 4, m = 6. 2 2
= ( (4; 4)) = = = ≈ 6,238.
3 2
6(4; 4) = ≈ 0,16.
3) τ = 1 = 4 , t 0 = 8, k = 5. 2 2
= ( (8; 4)) = = = ≈ 7,104.
( (8,4) ≥ 5) 6 2
( (8,4) ≥ 5) = 1 - ≈ 0,836.
4) τ = 2 , t 0 = 0, m = 0.
= ( (0; 2)) = = = ≈ 1,903.
4 2
p0 (0, 2) = ≈ 0,149.
5) τ = 2 , t 0 = 5.
= ( (5; 2)) = = = ≈ 3,127.
7 2
( (5,2) ≥ 1) = 1 - ≈ 0,956.
6) τ = 3 = , t 0 = 9.
= ( (9; )) = = = ≈ 0,747.
(1) 5
P (T (9) ≥ ) = ℮- 0,747 ≈ 0,474.
7) τ = 2 = , t 0 = 6.
= ( (6; )) = = = ≈ 0,45.
P (T (6) < ) = 1 P (T (6) ≥ ) = 1 ℮- 0,45 ≈ 0,362.►
13. , , , t : λ(t) = .
. 1 .
6(0; 1) ≈ 0,086;
6(1; 1) ≈ 0,115;
( (2,1) ≥ 5) ≈ 0,482;
p0 (0, ) ≈ 0,176;
( (1 , ) ≥ 1) ≈ 0,879;
P (T (2 ) ≥ ) ≈ 0,452;
P (T (1 ) < ) ≈ 0,246.►
.
14. . . , , , . . : () = 1 σ () = 4 .
, , , k ; , .
, .
() = 1 , σ () = 4 = . 2 5 3
= λ = = = 1 ( ).
7 2 3
σ () = = =
k = = ≈ 3.067.
k , k . k , .. k = 3.
, =1 .
3 3
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= = 13,5∙ t 2∙℮-3 t (t > 0).
, ,
1) (0, +∞),
2) ,
3) ;
4) t = , =0,812,
5) t 1 = t 2 = , 0,287 0,575 ,
6) = 0, .. 0 t .
= , , ,
= = = 13,5 .
= 13,5∙ + 13,5∙ =
= 13,5∙0,003+13,5∙ =13,5∙0,003+13,5∙0,17 = 0,189.►
15. , , () = 1,5 σ () = 1 . , .
. = .
= ∙ t ∙℮-2 t.
≈ 0,404.►