- , . , , .
f(t):
;
;
-
;
( );
-;
;
c2 - ;
- .
n A m (). A p, A q=1-p; m, n
,
- m n.
:
1) n - ;
2) mp;
3)
.
n/m p(1-p)/m.
(. 1) X , X , . , , .. () .
f(t) = xp[-(t-T)2/2s2],
T - ; s - () .
t
F(t)= xp[-(t-T)2/2s2].
F(t) .
F (t) = 0,5 + (u) = Q(t); u = (t-T) / s.
t
P( t) = 1-Q(t) = 1-[0,5+(u)] = 0,5 - (u).
l(t) . 1. T :
y=(t-T)/s.
- .
. t:
F (t) - , .. , ,
P (t) - , , ( ).
:
; - g-;
- ; - ; - ; -
|
|
(. 1). -¥ +¥, ,
f(t) = xp[-(t-T1)2/2s2].
T1
T = T1 + f(t) = .
T/s ³2, , c .
P(t) = .
l(t) = .
- (g-)
(. 1). , k , l0,
f(t) = ,
l0 - , k . .
k , .. ,
P(n³k) = 1 - p(- l0t).
t
f(t)= = .
: T1 = kT0 = k/l0.
P(t) = xp(-l0t) .
k = 1 g- .
k g- , .
. , , , . 1.
:
f(t) = lata-1xp(-l0ta).
t
P(t) = xp(-l0ta).
l(t) =al0ta-1.
a l0 - . l0 , . a = 1 ; a < 1 ; a > 1 - . a l0, .
, (, ). , . , - .
, .
|
|
(a = 1,4 - 1,7).
:
T = .
(-) .
-
p(x) = x/ s2 exp(-x2/2 s2) x > 0;
p(x) = 0 x£0,
s > 0. , x = s. .
g-, .
( ) :
f(t) = t/ s2 xp(-t2/2s2)
P(t) = xp(-t2/2 s 2)
l(t) = t/ s2
= .