, . .
:
1) , ;
2) , ( ).
, : , . n . , n ; $$ (.. ). $$ $$, .. $p=P(A)$, ( $$ ) - $q=P(\overline{A})=1-p$.
, n k ,
Pn (k)= Ckn ⋅ pk ⋅ qn − k, q =1− p.
( ) .
10. . .
U, (). gi U ξi. , (-∞ < x < +∞) g, ξ < x, , .. {ξ < x} = P(A) = F(x). ξ , F(x) -
:
- F(-∞) = 0
- F(+∞) = 1
- F(x) -
, .. (, ). F(x) - .
.. (, ; , ). F(x) , . .
F(x), (), (i) . , . -, . : y 2 1 -1 0.5; z = -y .
-, , .., , () , . .
|
|
, . , , .
1.
, (a,b), (a,b) , (a,b) 0.
6.1
: a, b
2.
,
(6.1)
. ( 6.2)
: a, σ
6.2
3.
, , , , ( ).
(6.2)
n - , m - ( ), n(m) - , m , q = 1 - ( , ).
1: 5 , , 6 ?
n = 5, m = 2, p = 1/6, q = 5/6
: n,
4.
, , n , , : n = .
11. .
, , , .
:
1) ;
2) , ;
3) 10 .
X
x, F (x) .
, , p (x), ..
ρ (x).
1. ρ (x) ≥ 0 .
2. :
, ,
F _ (x) ρ (x), b
a ρ (x) dx = F (b) − F (a), x 1 = a, x 2 = b , F (b) − F (a) = P (a ≤ X < b), .
3.
( ).
|
|
A{−∞ < X < + ∞}.
4. F (x) ρ (x)
, F (x) ,
F (x) = P (−∞ <X < x},
a = −∞, b = x ,
4 .
5. C
Δ x,