n , p.
, , , , . .
,
29
.: X1 2 ( ) . 1+2 , , .
1: , 1,2
, . .. 1 2 : =>
.. p - B(n,p) .
2: ,
, . .. 1 2 : =>
3: , 1,2
, =>
30 :
: Y ( ):
ov[X,Y] = M[(X-M[X])(Y-M[Y])]= M[Ẋ,Ẏ].
-:
1) ov[X,Y] = ov[Y,X]
2) ov[X,X] = D[X]
3) ov[X,Y1+Y2] = ov[X,Y1] + ov[X,Y2]
4) ov[C*X,Y]= C* ov[X,Y]
5) D[X+Y]=D[X] + D[Y] + 2 ov[X,Y]
6) |ov[X,Y]| ≤
0≤ D[tX+Y] = t^2*D[X] + D[Y] + 2t*cov[X,Y]
= 4 (ov[X,Y])^2 4* D[X]*D[Y] => |ov[X,Y]| ≤
31 .
: :
-:
1)
2) X Y => ( )
cov[X,Y]=M[XY] M[X]M[Y] = | Y |= M[X]M[Y] M[X]M[Y] =0 =>
3) Y=aX+b,
M[X] = m, D[X]= M[Y] = am+b, D[Y]=
cov[X,Y] = M[(X-m)(ax+b (am+b))] = a* M[(X-m)^2] =
: X Y , . Y . . Y. . - . - , .
32
: Xi , . (-) n -
-:
1) M[Y]=n; D[Y]=2n
2) (: f (x) )...n2>n1 n2 n1
: . . . Y : n . .
1) (: St (x) )...n1>n2 - n2 n1
2) St(0,1) N(0,1)
: - . n1 n2
-: Fn1,n2,p F(n1,n2) p, Fn1,n2,(1-p) = 1/ Fn1,n2,p
33
1 (1 ):
|
|
, .
, ;
2 (2 ):
- , , .
. :
34 ( ):
: , . a (), ( )
:
: . , .. .
, , . :
35
1)
. (*).: .
2) - . . , . (*).
, .
3) , . - n p. , .
Xk | ||
p | q | p |
(2)
36
: - . , , . - . : .
:
:
1) - .
2) -
3) ,
.
:
1) n - , .. , .
2) (2) . , , (3) n :
, .. .