= k/n , k n .
0,999 ()
= k/n = X/n - n .
M[h] = M[X/n] = 1/n*np=p
D[h] = D[X/n] = 1/n2*D[X]= 1/n2*npq=pq/n
= k/n = X/n = X1/n + + Xn/n~N(p, pq/n)
10. -. -.
- -.
(F) W, W={ω1,,ω2,} .- : 1. ΩÎF, ÆÏF; 2. A,BÎF => A+B 
F, ABÎF, Î F; 3. F 
- - , . .
F, () -, , -:
1.P(Ω)=1; 2.Î,()≥0; 3.∙≠0, A+BÎF=>P(A+B)=P(A)+P(B).
=ÆÞ 
: 1.(Æ)=0 -- 2. 
3. Ì- - , ()<=(). 4. P(A+B)<=P(A)+P(B) 5. :
1Ì2ÌÌnÌ, 
;
1É2ÉÉnÉ, 
-, : ()=./.Ω. .. - - , > , > . P(A)=mes(A)/mes(Ω) /S.
14.. .
M[X]=mx= 
M[Y]=my= 
(M[X], M[Y])- . X Y - . . . . . . . M[X+Y]=
M[X]+M[Y] X Y- . . . XY . . M[XY]= 
=M[X]*M[Y].
. . , . , , . X Y- . , (1). . . d. X , Y Y = yj, : M[X/Y=yj]=
: D[X+Y] z=X+Y => D[z]=M[(z-mz)2], mz=mx+my
D[z]= M[((X-mx)+(Y-my))2]= M[(X-mx)2]+2 M[(X-mx)(Y-my)]+
+M[(Y-my)2]=D[X]+2cov(X,Y)+D[Y]
: D[XY]=D[X]+D[Y]2cov(X,Y) X Y , cov(X,Y)=0 => D[XY]=D[X]+D[Y] D[aXbY]=a2D[X]+b2D[Y]2abcov(X,Y)
: 1. : 
. . M{} . . M{}2.
-:
M[X+Y]=M[X]+M[Y] M[X*Y]=M[X]*M[Y], X Y D[X+Y]]=D[X]+D[Y], X Y
3.
4.
(- 13, - 15)
17. .
(X,Y) f(x,y), .
|
|
|
. X, f1(x), f(x,y) y:
Y,f2(y):
(1) , (1) X Y , M[X]=m1, D[X]=σ12, M[Y]= m2, D[Y]=σ22
X Y
cov(X,Y)=M[(X-m1)(Y-m2)]= = 
, ρ (1)
-:
1. (X,Y) . .:
.
2. ρ=0 => f(x,y)= f1(x) ´ f2(x) => X Y
3. :
f(X/y) f(Y/x)
f(x,y) (1) . xOy (m1, m2) .
Z=f(x,y) , xOy, , -:
, λ const. xOy . .. f(x,y) , .
