.
, , .
, .
() , , .
+ A È (: ). + , , .
() , , .
, ,
Ç (: ). , , .
, .
, , N:
= M A/ N. (1.3.1)
, . , W. : (W) = 1.
, . Æ. : (Æ) = 0.
:
1. : 0 £ £ 1.
2. :
( + ) = () + (). (1.3.2)
1- : .
, .
: , , :
( ) = () (). (1.3.3)
:
( + ) = () + () ( ). (1.3.4)
.
1. , 2 . , 7. , 8. ?
. ( ) , . W . W1 = (1, 2, 3, 4, 5, 6) W2 = (1, 2, 3, 4, 5, 6). W 36 , .
|
|
( ) 6 (1,6; 6,1; 2,5; 5,2; 3,4; 4,3), ( ) 5 (1,6; 6,2; 5,3; 3,5; 4,4). 36. (1.3.1), : P() = 6/36, () = 5/36. , .
2. 5 10 , 3 17 . , .
. , . (1.3.1) : () = 5/15 = 1/3; () = 3/20.
. (1.3.3) : ( ) = () () = (1/3) (3/20) = 1/20.
: 1/20.
3. 5 10 , 3 17 . , .
. (), () ( ), (1.3.4), : ( + ) = 1/3 + 3/20 1/20 = 22/60.
: 22/60.
X
1 + 2 + + n = 1. (1.3.5)
X:
(X) = . (1.3.6)
( , ).
X:
D(X) = (1.3.7)
( ).
X .
X:
f X(x) = f (x) = d P/ dx.
X:
F X(x) = F (x) = P (X £ ),
P(x 1 < X < x 2) = F (x 2) F (x 1). (1.3.5)
:
f (x) = F (x)' = dF (x)/ dx,
F (x) = .
:
= l.
X:
() = .
X:
D(X) = .
:
D(X) = {[ ()]2}
D(X) = ( 2) [()]2.
:
s () = Ö(X).
( ):
f (x) = ,
, s .
:
F (x) = (t), (1.3.6)
t = ( )/ s, (t) .
[ , b ]:
f (x) = 0 [ , b ],
f (x) = 1/(b ) £ £ b.
:
f (x) = l ( lx), ³ 0.
:
n = n 0 exp ( mgh / kT),
n , h , m , k , g .
|
|
4. ( = 0) . , :
) s < X < + s; ) 2 s < X < + 2 s; ) 3 s < X < +3 s.
s.
(1.3.5) (1.3.6) :
( s < X < + s) = F (s) F ( s) = [(s )/ s ] [( s )/ s ],
[(s 0)/ s ] = (1) = 0,8413 ( ),
[( s 0)/ s ] = ( 1) = 1 (1) = 1 0,8413 = 0,1587,
= (1) (1) = 0,8413 0,1587 = 0,6826.
.
10 000 27 ( 3 s, + 3 s). , X , .
5. X 3 4. , 1 < X < 7.
. = 3, s = Ö4 = 2 ( ):
(1< X < 7) = [{(7 3)/2} {(1 3)/2}] = [(2) (1)] =
= (0,9772 0,1587) = 0,8185.