3.
s . (s ). ln =l (n³0), mn = nm n £s, mn = sm n ³ s. .
() :
n = 0(l/m)n / n! (n £ s), (2.6.9)
n = 0(l/m)n / s!/sn-s (n ³ s), (2.6.10)
(2.6.11)
, :
= 0(l/m)s+1/(s1)!/(sl/m)2, (2.6.12)
, ,
n = +l/m, (2.6.13)
:
= /l. (2.6.14)
. W.
W= 0(l/m)s/s!. (2.6.15)
, t. (>t).
(>t)=emt(1+(W/s)(1 emst(1l/ms1/s))/(1l/ms1/s)). (2.6.16)
, . , l/m<<1 0 1 l/m, (l/m)s+1/s2, l/m, 1,
0 (s l/m)(s 1)! /ss (l/m)/(s l/m).
2.6.4. 3 (), . , l = 5 m =6. l/m =0.833, s =3
0 = 1/(0.8330/0!+0.8331/1!+0.8332/2!+ 0.8333 /(3!(1 0.833/3))) = 0.432,
=0.432×0.8334/2!/(30.833)2 = 0.022,
=0.022/5 = 0.0044 .(16 .)
, 43.2% , 16. , () . , :
1 =0.40, 2 =0.15, 3 =0.04.
2 .
0 = 1/(0.8330/0!+0.8331/1!+ 0.8332 /(2!(1 0.833/2))) = 0.412,
= 0.412×0.8333/1!/(20.833)2 = 0.17,
= 0.17/5 = 0.034 .(2 .)
41.2% , 2 .
2.6.2, 17%, 50 . W (>t) . 1 =0.34, 2 =0.14, 3 =0.06.
4.
, , k. ln =l 0≤n < k+s ln =0 n ³ k+s; mn = nm n£s, mn = sm s ≤ n ≤ s+k.
:
n = 0(l/m)n / n! (n £ s), (2.6.17)
n = 0(l/m)n / s!/sn-s (s ≤ n ≤ s+k), (2.6.18)
, l/m≠s, (2.6.19)
, l/m=s, (2.6.20)
, :
|
|
=0(l/m)s+1(1(l/ms)kk(l/ms)k(1l/ms))/(s1)!/(sl/m)2, l/m≠s, (2.6.21)
=0(l/m)sk(k+1)/(2s!), l/m=s, (2.6.22)
:
= /l/(1 k+s). (2.6.23)
2.6.5. (k=2 s=2). :
0=1/(0.8330/0!+0.833/1!+0.8332(1(0.833/2)2+1)/2!/(10.833/2)) = 0.423,
=0.423×0.8333(1(0.833/2)22(0.833/2)2(10.833/2))/1!/(20.833)2=0.25,
=0.25/5/(1 2+2)= 0.25/5/(1 0.423×0.8334 /2!/22)=0.05 .
, , l=12, l/m=2= s
0=1/(20/0! +2/1!+22(2+1)/2!)= 0.111,
=0.111*22*2*3/(2*2!)=0.67,
=0.67/12/(12+2)=0.67/12/(10.111×24/2!/22)=0.07 .
11.1%, 0.07×60= 4.3 .
, 3 4.
2.6.6.
1. 4 . l=20 , 11.5 . (m=60/11.5=5.217), l/m=20/5.217=3.83 s=4. (2.6.11):
0 = 1/(3.830/0!+3.83/1!+3.832/2!+3.833/3!+3.834/4!/(13.83/4))=0.0042.
(2.6.12)(2.6.14) :
=0.0042×3.835/3!/(43.83)2/20= 1 .
(2.6.15):
W= 0.0042×3.834/4!=0.886.
, t=0.5 (30 .). (2.6.16):
(>0.5) =e5.217/2(1+0.886/4)(1e5.217×4/2(13.83/41/4))/(13.83/41/4))=0.7.
, 88.6% , 70% (, ).
2. 1 . k=16, (2.6.19)
0=1/(1+3.83+3.832/2!+3.833/3!+3.834(1(3.83/4)17)/4!/(13.83/4))=0.00759
, , (2.6.21)
=0.00759×3.835(1(3.83/4)1616(3.83/4)16(13.83/4))/3!/(43.83)2=5.82.
20=3.8320×0.00759/4!/416=0.03397, (2.6.23), :
=5.82/20/(10.03397) =0.301 .(18 .)
1 2, , , , 3.4% (20=0.03397).