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:




:

































 

 

 

 





: ()= , 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.

 

 





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: 2016-10-30; !; : 544 |


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