E[h(Y)|X=xi]=(j=1..m)(h(yj)P(Y=yj | X=xi)
X=xi : g(xj)=E[Y | X=xi], g(x)=E[Y|X] - Y X/
.
n . : A1, , Ak , xj Aj n , (x1xk)T . :
P(X1=m1Xk=mk)=n!/(m1!...mk!)(j=1..k)(pjmj)
M[ ]=n()
j1<>j2:
M[xj1xj2]=n(n-1)pj1pj2-npj1npj2 = -npj1pj2
.
N , D1 1- ,, Dk k- . n . xj j- , (x1xk)T :
p(x1= m1xk= mk)=
.
- .
.
,
.
1) =1
2)
3)
4) m<k:
.
F(x, y) (X, Y), B R >0:
B={x:x<=X<x+Δx} Δx>0:
.
=
.
.
1) M[C]=C
2) M[kX]=kM[X]
3) M[X1+X2+Xn]= M[X1]+M[X2]++M[Xn]
4) M[XY]=M[X]M[Y] X, Y -
.
1) D[C]=0
2) D[X+C]=D[X]
3) D[cX]=c2D[X]
4) D[aX+b]=a2D[X]
5) X, Y: D[X+Y]=D[X]+D[Y]
.
1) X, Y , K(X, Y)=0
2) |K(X,Y)|<=sqrt(D[X]D[Y])
.
1) X Y , r(X, Y)=0
2) |r(X,Y)|=1 (?)
, , .., .
(?)
.
1)
2)
3) -
,
, , .
Z=XY,
, .
. , .
- .
|
|
.. , () TϵR
t-, =
- , .