, a=0, : |
X - ( ), |
: |
: |
, , 10, 0,9544. , 95,44% , , . |
336, , 30 8, . X Y ( ) , , 6 4, , . : ) ; ) , , , . |
, : |
, X , |
- . |
, |
, : |
, a=0, : |
: X, : |
) X Y - , x (-15,15) - , y - (-4,4) - . , : |
X Y - , |
, .. |
, 0,6741. |
) , . - , . , - . p = 0,6741, q = 1 - p = 1 - 0,6741 = 0,3259. , , : |
, , , : |
337 X a=10. X (10,20) 0.3. X (0,10)?
:
x=a=10, , (0,10) (10,20), . X , :
|
|
P(0<X<10)=P(10<X<20)=0.3
: 0.3
338 X a=25. X (10,15) 0.3. X (35,40)?
:
x=a=25, , (10,15) (35,40), . X , :
P(10<X<15)=P(35<X<40)=0.2
: 0.2
339 , :
.. t , X-a X .
:
: =>
:
...
340 : , , 0.9973.
:
, 339, :
t=3, :
, , , .
, , :
...
341 X a=10 . , , 0.9973 X .
:
, , , t=3.
:
:
:
:
342 X , , 0,9973 X .
:
, , , t=3.
:
:
, 30 .
: 30 .
343 - , X. , X X a=10 . , , 0.9973 .
:
:
, , , , t=3.
:
, :
, :
:
344 X
X.
:
Mo(X) X, . , X=a
f (a)=0; X<a f (a)>0, X>a f (a)>0; , X=a , , Mo(X)=a
Me(X) X, f(X) , . ( f(X)) X=a, f(a) , . , Me(X)=a.
|
|
, .
345 X , a=0 , X , ( .
:
:
,
:
346 ,
:
F(x) =
:
F(x) =
347 ,
:
F(x) =
:
F(x) =
348 : a) f(x)=0 x<0, x ) F(x)=0 x<0 x
:
, :
, , ,
,
) , :
, , ,
,
: a) 2; b) 0.4
349 , , (a,b) - .
: F() = 1 - . (,b).
P(a < X < b) = f(b) f(a) = [1 - ] [1 - ] = -
350 , f(x) = 3 ≥ 0; < 0 f(x) = 0.
, (0.13, 0.7)
:
P(a < X < b) = - . , , , = 0.13, b = 0.7, λ = 3, , :
P(0.13 < X < 0.7) = - = - = 0.677 0.122 = 0.555
351 , ≥ 0 f() = 0.04 ; < 0 f() = 0.
, (1,2).
:
P(a < X < b) = - (. 350 ). = 1, b = 2, λ = 0.04 , :
P(1 < X < 2) = - = -
352 , f() = 1- ; < 0 f() = 0.
, (2,5).
:
P(a < X < b) = - (. 350 ). = 2, b = 5, λ = 0.6 , :
P(2 < X < 5) = - = -
1 - -
353
F(x) = λ (x ≥ 0); f(x) = 0 (x < 0).
:
() = .
, f(x) = 0 < 0 f(x) = λ ≥ 0, M(X) =λ .
:
- ,
u =, dv = dx , () = 1/λ.
354 , ≥ 0:
) f() = 5 ;
) f(x) = 1 -
356 :
) ;
) , : f(x) = λ ≥ 0; f(x) = 0 < 0.
:
)
D(X) = .
, f(x) = 0 < 0, () = 1/λ D(x) = λ dx
, λ dx =
|
|
,
D(X) = 2/ 1/ = 1/
) :
σ() = = 1/λ
357 , : f(x) = 10 .
:
, :
D(x) = λ dx
, λ dx =
,
D(X) = 2/ 1/ = 1/
0.01
σ() = = 1/λ
0.1
358 , : f(x) = 1 - ( ≥ 0)
:
σ() = = = 2.5
D(x) = = = = 6.25
359 , f(x) = 0 x < 0, f(x) = C ≥ 0; , .
.
:
dx = 1
-λC
360 3= M[X M(X)]3 .
.
, : 3= M[X M(X)]3=M(X3- 3X2M(X) + 3XM2(X) M3(X))= M(X3) 3M(X2)M(X) + 3M(X)M2(X) M3(X) = M(X3) 3M(X2)M(X) + 2M3(X)
()= 3= M(X3) 3M(X2) + 2
M(X3): M(X3) = = = = =
= = = = = = = )=
, M(X3) =