: , , , , , , - . , , , .
.
, : , , , , . .
: , , ( ) .
. , . X, 2,..., (1) p1, (2) = 2 . . X (. 1).
1
X | 1 | 2 | 3 | 4 | 5 | |
p1 | p2 | 4 | 5 |
(2.9) |
(. 2.1), :
, . (2.9) .
* , . (. 2).
2
X | ||||||
1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 |
* . 49. (. 3).
3
X | |||||
1/49 | 1/49 | 1/49 | 1/49 |
. l (l , 0, 1, 2 3). (); , , . . , [1 - ()].
l = 0 , . , (2.6),
( ) = [1 - () ] [1 - () ][1 - ()] = [1 - ()]3.
l = 1 , . (2.6)
( ) = () [1 - () ][1 - ()] = () [1 - ()]2.
|
|
l = 1 : ( ) ( ), , (2.4), l = 1, :
( , , ) = () [1 - () ]2.
l = 2 , . , , :
( , , ) = 2() [1 - () ].
l = 3 . ,
( ) = 3().
, (. 4).
4
l | 2 | |||
[1- () ]3 | () [1 - () ] 2 | 2() [1 - () ] | 3() |
, l :
(2/10)
= (); - l,
* 0,5. , ; () = 0,5, = 6, l = 4.
(2.10):
. , , , . .
( ) :
(2.11)
X x1, x2,..., 1, 2, , .
n , 1/, 2/,... , . .
* ,
(. . 2).
(2.11):
() = 1 1/6 + 2 1/6 + 3 1/6 + 4 1/6 + 5 1/6 + 6 1/6 = 7/2 = 3,5.
*
, (. . 3).
(2.11),
() = 1 1/49 + 2 1/49 +... + 49 1/49 = 25.
, (), (). ? , X - (), ( ) : [ - () ]. , , , . [ - () ], [ - () ]2. , .
|
|
:
D(X) = [ - () ]2 (2.12)
D(X) = (2) - [ () ]2. (2.13)
, X .
* ,
(. . 2).
3,5. : (1 - 3,5)2 = 6,25; (2 - 3,5)2 = 2,25; (3 - 3,5)2 = 0,25; (4 - 3,5)2 = 0,25; (5 - 3,5)2 = 2,25; (6 - 3,5)2 = 6,25. (2.12) (2.11) :
D(X) = 6,25 1/6 + 2,25 1/6 + 0,25 1/6 + 0,25 1/6 + + 2,25 1/6 + 6,25 1/6 = 2,9167. , (2.13):
[ () ]2 = 3,52 = 12,25; (2) = I2 1/6 + 22 1/6 + 2 1/6 + 42 1/6 + 52 1/6 +
+ 62 1/6 = 15,1667;
D(X) = 15,1667 - 12,25 = 2,9167.
(2.12), . , , :
(2.14)
. , . .
dP , X + dx. , dx, dP: dP ¥ dx. , , ,
dP = f(x)dx, (2.15)
f(x) , . , , dx , :
f(x) = dP/dx. (2.16)
(2.15) , , - (ab):
(2.17)
(2.18)
:
(2.19)
(2.19), , , :
(2.20)
(2.21) (2.21)