? ,
A B , A B
B()=() . ()=()*()- .
=+ Þ ()= ()+(), ()=()+()(). ()=()[1-()], ()=()()
2. .
1, 2,3,., n, . 2 (), ., n () . .
, 1, 2,,n, , :
() = (1) 1() + (2) 2() +.+ (n) n().
.
, , 1,2,,n. , , , 1, 2,, n. ,
() = (1) + (2) +.+ (n) (1)
. :
(1) = (1) 1(); (2) 2(): . (n) = (n) (bn) ()
(1) :
() = (1) 1() + (2)2 () + .+ (n) n ()
3. .
1,2,,n, . , , . :
() = (1) 1() + (2)2 () + .+ (n) n () (1)
, , . , , , , . ,
(1), (2),., (n).
(1).
(1) = () (1) = (1)1()
(1) = (1)1()
()
() (1),
pA(Hi)= i(A)p(i).
1(1)(1)+2()(2)++n()(n)
, , .. i (i= 1,2,,n)
(i) = (i) i()
(1) 1() + (2) 2()+.+(n) n()
. , , .
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|
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n .
2 n(k) n(k+1). , 1<2, 2<1. n(k)/ n(k+1)<>=1.
n(k)=nkpkqn-k; Pn(k+1)=Cnk+1pk+1qn-k-1. Cnk+1=nk*(n-k)/(k+1). - (k+1)/(n-k)<>=1. (k+1)*q<>=(n-k)*p. - k<>=n*p-q. np-q a. - k<a-1 Pn(k)<Hn(k+1), k=a-1 ( ) Pn(k)=Pn(k+1), k>a-1, Pn(k)>Pn(k+1). k<a-1 Pn(k) , k>a-1, . , - , - , k, k=[a]=[n*p +p]. =, 2 k=a-1, k=a.
- : X . , M(X)=m D(X)=a, " e>0 -
P(|X-m|³e) £ D(X)/e2. : 1 - P(|X-m|³e) ³ 1 - D(X)/e2; P(|X-m|<e) ³1 - D(X)/e2.
3s: e=3s: P(|X-m|<3s) ³ 1-s2/9s2 = 8/9.
