, , , .
: . .
: , 10 .. :
[ = i] = pi, I = ,-1, 0, 1, ,
,
i , ,
pi ,
i .
[ = i], , , ( ).
, i i.
xi | x1 | x2 | x3 | xn | |
pi | p1 | p2 | p3 | pn |
- , 1+ 2 + 3 +... + n = 1.
.
:
1. 1000 . 1 1000 ., 4 500 ., 5 400 . 10 100 . .
: ( ) :
1 = 1000; 2 = 500; 3 = 400; 4 = 100; 5 = 0.
:
1 = 0,001; 2 = 0,004; 3 = 0,005; 4 = 0,010; 5 =1 ( 1+ 2 + 3+ 4),
5 =1 0,020 = 0,980.
:
xi | |||||
pi | 0,980 | 0,010 | 0,005 | 0,004 | 0,001 |
.
2. 3 , 2 1 . 2 . . .
: 3 1 , 1 . 1 2. 1 1 1 1 .
(1) = (2) =
, i 1. , . ( ):
xi | 1 | 2 |
pi |
. F (x), (); () = F (x).
|
|
: , , , .
F(x) , , .. F(x) = [ ≤ ].
, F (x) 0 1. , , (x 1, x 2)
(*) [ x 1< <x 2] = F (x 2) F (x 1), .. .
:
1. :
F (x) =
) F (x),
b) (0,25; 0,5).
:
)
b) (*) :
[0,25< < 0,5] = F (0,5) - F (0,25) = (0,5)2 (0,25)2 = 0,25 0,0625 = 0,1875.
F (x). . :
F (x) = 0 < x 1,
F (x) = p 1 x 1 ≤ < x 2,
F (x) = p 1 + p 2 x 2 ≤ < x 3,
F (x) = p 1 + p 2 + p 3 x 3 ≤ < x 4,
F (x) = p 1 + p 2 + p 3 +... + p n ≥ x n.
2. F (x) , .
:
F (x) = 0, < 0,
F (x) = p 1 = 0,0256, 0≤ < 1,
F (x) = p 1 + p 2 =0,1792, 1≤ < 2,
F (x) = p 1 + p 2 + p 3 = 0,5248, 2≤ < 3,
F (x) = p 1 + p 2 + p 3 + p 4 = 0,8704, 3≤ < 4,
F (x) = p 1 + p 2 + p 3 + p 4 + p 5 = 1, ≥ 4.
, :
F (x) =
:
F (x)
0,9
0,5
0,2
0 1 2 3 4 x
, F (x) i, . i , [ = i], .. . .
F (x), (), (i) .
, . -, . : y 2 1 -1 0,5; z = - y . -, , .., , () , . .
. , , .
|
|
1. .
, (a; b), (a; b) , (a; b) 0.
2. () .
. . . , , , - .
. . , , ( ), .
, , , , , .
. - , - , .
(. 4).
3. .
, , , , ( ).
,
n - , m - ( ), n (m) - , m , q = 1 - ( , ).
: 5 , , 6 ?
: n = 5, m = 2, p = , q = .
4. .
. , n , np = λ, n (m) , n m , .
, .