: ()= , D(X)= .
4
.
<a,b> Ì R ( , ), . . F(x) . , F(- ¥) = 0, F(+ ¥) = 1, F(x) - . F(x) . . .
, () ( - ):
F(x) = F(x) - F(- ¥) =
, f(x) - , 1- .
, f(x) - - , , F(x),
F(+ ¥) = = 1
, f(x), , f(x) - : 1.( ).
F(b) - F(a) = P(a £ X < b) = P(a < X < b) = P(a < X £ b) = = P(a £ X £ b) = .
() D(X)
M(X) = , D(X) = .
D(X):
D(X) = M(X2) - (M(X))2 = - (M(X))2.
()
, - ¥ < x < +¥
Î R s > 0 . N(a,s).
= 0 f(x) (f(-x) = f(x)), OY, () = 0. f(x) N(a,s) f(x) N(0,s) ( ), () = .
D(X) =s2.
.
, (), D(X), P(-3<X<3).
. . ,
, = 2, s = 1. , ,
, M (X) = a = 2, D(X) = s 2 = 1.
P (-3 < X < 3) = F(3) - F(-3) = =
, .
|
|
() = 1() = = + ()
() - , .. (-) = - ().
(x1 < X < x2) = ,
s - . ,
P(|X| < 3) = 1(1) - 1(-5) = (1) - (-5) = (1) + (5) =
= 0,3413 + 0,5 = 0,8413.