.
: (;b), , f(x) 0 , ..
0 ≤,
f()= a<<b,
0 ≥b.
f(x) . 1
(. 1) (.2)
, , :
0 ≤,
F()= a<≤b,
0 >b.
. 2.
(a;b), :
M()= , D(X)= , σ()= .
1. [3;7]. :
) f(x) ;
) F(x) ;
) M(X),D(X), σ().
: , , =3, b=7, :
0 <3,
) f()= 3≤≤7,
0 >7
(.3):
.3
) 0 ≤3,
F()= 3<≤7,
1 >7.
(.4):
.4
) M(X) = = =5,
D(X) = = = ,
σ () = = = .
()
: () λ>0, :
0 <0,
f()= λ-λ ≥0.
, , :
0 ≤3,
F()= 1-e-λ ≥0.
f () F() .5 .6.
.5 .6
, :
M(X)= , D(X)= , σ ()=
, .
(a;b) :
(a<<b)= e-λ- e-λb
2. 100 . , , :
) ;
) ;
) , 120 .
|
|
: M(X)= =100, λ=1/100=0,01.
,
0 <0,
) f()= 0,01 -0,01 ≥0.
) F(x)= 0 <0,
1- -0,01 ≥0.
) , :
(X>120)=1-F(120)=1-(1- -1,2)= -1,2≈0,3.