F(x) , , , , .. F(x)=P{X < }.
F(x).
1. F(-∞)=lim(x→-∞)F(x)=0. , , F(-∞)=P{X < -∞}. (X < -∞) : F(-∞)=P{X < - ∞}=p{V}=0.
2. F(∞)=lim(x→∞)F(x)=1, , F(∞)=P{X < ∞}. < ∞ . , F(∞)=P{X < ∞}=p{U}=1.
3. , [Α Β] . P{Α ≤X<Β}=F(Β)-F(Α).
4. F(x2)≥ F(x1), x2, > x1, .. .
5. . FΨ(xo-0)=limFΨ(x)=FΨ(xo) → xo
, , , , . X F(x), x ,
X , x
F(x) = P(X < x). (8.1)
F(x) . , X x. ( ) ϕ(x) X
ϕ(x) = F' (x)
f(x) F(x).
, .
ϕ(x), F(x), , .
. , . :
,
,
:
,
, , .