. p (x),
F(x)=P{ X < x }-∞∫x p (t) dt
, , . p(x) X, F(x)
. . . . . X -∞ ∫ ∞ x p (x) dx, p (x) . . X.
. . . . X -∞ ∫ ∞ (x-MX)2 p (x) dx, p (x) . . X.
. 2- X Y, - ., 2- p(u,v), x y :
P{ X < x,Y<y }-∞∫x-∞∫y p (u,v) du dv.
. 2- X Y . (X-MX) (Y-MY), :
v (X,Y)=-∞ ∫ ∞ -∞ ∫ ∞ (x-MX)(y-MY) p (x,y) dxdy
. . 2- . . . X Y
ρ (X,Y)=(Cov(X, Y))/√D X D Y
10. . . -, -.
: 1. ( + Y)= + MY (). : 
= 
, 
= 
. Σ - MX + MY = 
= ( + Y)■ 2. ( 1+ 2++ n)= 1+ 2++ n.(. 1). 3. = const, =. 4. - - Y , (Y)= MX + MY. : .. Y -, P (x i, y j)= P (x i) P (y j). (Y)= 
= 
= MշMY ■ 5. | (Y)| 
(- -). : " - - 0 £ ( + Y)2= a 2 MX 2+ 2 aMXMY + MY 2 . ). . . £ 0. D/4=(M (XY))2 - MX 2 MY 2 £ 0 Þ | (Y)| 
■ - MX DX - . - . . . - .
DX: 1. DX ³ 0. : P (X) ³ 0, MX 2 ³ 0 Þ DX ³ 0. 2. D = 0, = const. : = , () =1Þ D = M (C M)2 = M (0)=0 1=0■ 3. - ., . D (X) = 2 DX. : D (X) = M (X M (X))2= M (X MX)2= M [ 2(XMX)2]= 2 M (XMX)2 = 2 DX ■ 4. DX = M (X 2)(MX)2. . . - = . - . - . - . - . : DX = M (X MX)2= M (X 22 XMX +(MX)2)= M (X 2)2 M (X MX)+(MX)2= M (X 2)2 MX MX +(MX)2= M (X)2(MX)2■
. $ - - () - . - F(X)=P{ X < x }= 
. -, - - - . - () - - . - , - F(X) - . , . F(X) -: - -: 1. () ³ 0. 2. 1< 2, { 1< X < 2}= 
3. 
=1( -). - - () - . . . =1.
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. - . . . - Y, - - - , - - - (u, v), "u, v - { X < , Y < y }= 
