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- P (A) = , n , m ;
Pn = n! - n
(n! = 1 ∙ 2 ∙ 3 ∙ ∙ n, 0! = 1);
m n
(m ≤ n);
m n
(m ≤ n, );
+ , ;
∙ , ;
;
( + ) = () + () ;
( + ) = () + () − ( ∙ ) ;
( ∙ ) = () ∙ () ;
( ∙ ) = ()∙ , ,
;
n ,
|
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(A) = p , () = q, p + q = 1;
() = - , Hi ,
, Hi;
- , .
.
():
X x 1, x 2,....;
- :
xi | x 1 | x 2 | .... |
Pi | P 1 | P 2 | ... |
- , ();
- F (x) = P (X < x) = F (a) + P (a ≤ X < x) ;
- ;
- : M () = C, M (hX + C) = h ∙ M (X) + C;
- D (X) = M (X − M (X))² = M (X ²) − M ²(X);
- : D (X) ;
- : D (X) ≥ 0, D (0) = 0, D (h ∙ X + c) = h ² ∙ D (X);
- ;
.
1. : X = k = 1, 2, 3...
,
2. (): X = k = 0, 1, 2,....., n
M (X) = n ∙ p, D (X) = n ∙ p ∙ q, ;
3. : X = k = 0, 1, 2,..., n
M (X) = a, D (X) = a,
():
X ;
- ( ) :
- :
F (x) = P (X < x) = , ;
-
P (α < X < β) = F (β) F (α) =
- M (X) =
- D (X)
- .
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1. (a, b)
a x b,
,
M (X) = D (X) = , ;
1.
M (X) = , D (X) = ,
2.
F (x) = 0.5 + (), (z) = ( );
M (X) = a, D (X) = , ,
P (α < X < β) = .
.
1. , . , .
P = , n = P 4= 4! = 24, m = 2! ∙ 2! = 4 => P = = = 0.17.
2. , , , . , ?
n = , m = (4∙2 + 2) ∙ = P = = . 3. , 4 7 , 5 . , 2 ?
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1. 5 6
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2. a) P ( ) = = 0.11.
) P ( ) =
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=> P () = 1 − P () = 1 0.31 = 0.69.
) , 5 6
P (A) = 1 P () = 1 P ( ) = .
3. ) ( ) = = 0.085.
) P (, , ) = = 0.24
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H 3 − 1 2 ;
H 4 3 .
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1. :
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) , - :
0,14 | 0,23 | 0,38 | 0,26 | 0,19 | 0,06 |
:
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2.7 | 3.5 | 4.3 | 5.1 | 5.9 | 6.7 | |
0.11 | 0.18 | 0.3 | 0.21 | 0.15 | 0.05 |
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2.7 | 7.25 | ||
3.5 | 19.08 | ||
4.3 | 29.02 | ||
5.1 | 25.45 | ||
5.9 | 1.29 | 12.91 | |
6.7 | 2.03 | 3.78 |
:
7.25 | 1.94 | ||
19.08 | 0.06 | ||
29.02 | 0.03 | ||
25.45 | 0.78 | ||
12.91 | 0.34 | ||
3.78 | 0.39 |
, , ( - , - ). .
, .
2. X Y N = 100 :
yj xi | 5.3 | 7.4 | 9.5 | 11.6 | 13.7 | mxi | ||||||||||
2.7 | - | - | - | |||||||||||||
3.5 | - | - | ||||||||||||||
4.3 | - | - | ||||||||||||||
5.1 | - | - | - | |||||||||||||
5.9 | - | - |
: 2017-01-28; !; : 681 | : : - , 20 40 . - .
|
: 0.245 .