1. ( ) n , (. . 3). p. P .
: P=pn
2. n , (. . 4). p. P .
: P=1-(1-p)2
3. n , (. . 5). p. () p1. P .
: P=1-(1-p)*(1-p1*p)
4. n (. . 6), p. , - . : Pa, Pb.
: Pa=[1-(1-p)2]n Pb=[1-(1-p)n]2
5. n (. . 7), p, . , - , . P .
: P=[1-(1-p1)2]*[1-(1-p2)3]*p3*p4*[1-(1-p5)*(1-p6)]
6. 3- (. . 8). n1 , n2 . n3 . p. P .
: P1=pn1 P2=pn2 P3=pn3
P23=1-(1-pn2)*(1-pn3)
P= pn1*[1-(1-pn2)*(1-pn3)]
7. 2- U1 U2, , C (. . 9). C U1=p1, U2=p2. C U1=p1', U2=p2'. C=ps. P .
: P=ps*p1*p2+(1-ps)*p1*p2
8. 2- U1 U2, , C (. . 10). C U1=p1, U2=p2. C U1=p1', U2=p2'. C=ps. P .
: P=ps*[1-(1-p1)*(1-p2)]+(1-ps)*[1-(1-p1')*(1-p2')]
9. 2- U1 U2. t : U1 p1=0.8, U2 p2=0.9. t . , :
- H1 - U1
- H2 - U2
- H3 - U1 U2
: , H0, .
A=H1+H2+H3
() :
- P(H1)=(1-p1)*p2 =(1-0.8)*0.9=0.2*0.9=0.18
- P(H2)=(1-p2)*p1 =(1-0.9)*0.8=0.1*0.8=0.08
- P(H3)=(1-p1)*(1-p2) =(1-0.8)*0.9=0.2*0.1=0.02
- A=i=13*P(Hi)=P(H1)+P(H2)+P(H3) =0.18+0.08+0.02=0.28
() :
- P(H1/A)=P(H1)/A=0.18/0.28=0.643
- P(H2/A)=P(H2)/A=0.08/0.28=0.286
- P(H3/A)=P(H3)/A=0.02/0.28=0.071
10. m U1 n U2. t U1=p1, U2=p2. , t 2- U1 2- U2. .
: A ( ) 2- :
- A1 - ( 2- m U1 )
- A2 - ( 2- n U2 )
X1 U1 , m, p1. A1 , X1 2, :
|
|
|
P(A1)=P{X1>2}=1-P(X1<2)=1-P(X1=0)-P(X1=1)= 1-(g1m+m*g2m-1*p1), g1=1-p1
: P(A2)=1-(g2n+n*g2n-1*p2), g2=1-p2
:
R =P(A)=P(A1)*P(A2)= [1-(g1m+m*g2m-1*p1)]*[1-(g2n+n*g2n-1*p2)], g1=1-p1, g2=1-p2
11. 3- (. . 11). U1 n1 l1. U2 n2 l2. U3 n3 l2, .. U2 U3 . U1 2- . U2 U3, .. , . U1 U2 U3 . p. , t .
: U1, U2 U3 t :
p1=1-e-1*t p2=p3=1-e-2*t
U1 t :
R1=1-(1-p1)n1*n1*p1*(1-p1)n1-1
U2 U3 :
R2=1-(1-p2)n2 R3=1-(1-p3)n3
:
R=R1+(1-R1)*R2*R3
:
.. . , "", 1965 .
16503-70 - " . ".
.. , , , 1972 .
18322-73 - " . ".
13377-75 - " . ".
.., .. , , . , 1975 .
.., .. , , . , 1976 .
.. , , . , 1978 .
16593-79 - ". ".
. 08.2003 .
7.4. [1, 2]
