View
7
Download
4
Category
Preview:
DESCRIPTION
vaznije raspodele verovatnoca- hidrologija
Citation preview
1
2
- () -
:
:
( ) xnxn qpxn
xP
= ,...2,1,0=x( )!!
!xnx
nxn
=
pq =1
),(: pnBSn
3
- () -
: , .
21=p
211 == pq
( ) ( ) 81
21
21
!03!0!30
030
3 =
=
P
( ) ( ) 83
21
21
!13!1!31
131
3 =
=
P
( ) ( ) 83
21
21
!23!2!32
232
3 =
=
P
( ) ( ) 81
21
21
!33!3!33
333
3 =
=
P1/83/83/81/8P(x)3210X
4
- -
: n,
nh , :
: .
,...2,1,!
}{ == jej
jSPj
n
.0,,)( >= nn pnpAP
)(: PS,...2,1,0,
!}{ ==== k
kekXPp
k
k
2 5
- -
: . 1000 , 20 . 100 3 ?
3,202.0100 === kx
18.0!32}3{3
23 ==== eXPp
,...2,1,0,!
}{ ==== kk
ekXPpk
k
6
- -
X , :
. :
:
( ) ,...2,1,0,1}{ ==== kppqpkXP kk
( ) ,...2,1,0,1}{ === kppkXP k
( ) ,...2,1,1}{ 1 === kppkXP k
7
- -
: , -?
. -1 , - . ,
.
( ) ( )kkkXP 2/12/12/11}{ 1 ===
( ) pAPAPp c === 1)(
8
:
X (a,b], .
=< ba
dxxfbXaP )(}{
}{ bXaP 0 ), :
- :
: N(m, 2): =>
X*: N(0, 1) .
( ) ( ) 22 2/21
mxexf =( ) ( ) ( ) dtexFxXP x mt
== )2/(2
22
21
*
2Xmx =
10
- () - N(m, 2) :
f(x)
0
=0.5
>1
=5 x
21
11
- () -
: =>
X*: N(0, 1) .X* - (Z). - X* :
, - f(x) F(+h)=0.5 ;
*
2Xmx =
( ) >= x t xdtex0
2/ 0,21 2 ( ) ( ) 0,
4 13
- ()-
X Y=ln(X) . X=Y , Y: N(m,2) , 2 >0. :
( )( )
2ln
2
2lnln
ln 21
x
xx
x
ex
xf = 0, >x
0,0)( = xxf
0 1 2 3 4x
0.4
0.8
1.2
f(x)
y2=0.1
y2=2
y=0
y2=0.5
14
- - -
Y: N(m,2), Y=ln(X-x0), x0=const. X=eY+x0 X:
( )
>
=
02)ln(
0
0
,2)(
1
,0
)( 22
0
xxexx
xx
xf mxx
15
- -
X: U(a,b) , a
>
= baxeax
ab
xxf b
ax
b
5 17
- -
X: () . :
.
0,0,0,0
)( >
>= xe
xxf x
18
- -
:
-
0,0,0,)(
10,0
)( )(1 >
>
=
xex
xxf x
( ) .0,0
1 >= +
dtet t
19
- -
X III, :
- ( )
0,0,,)(
)(1
,0)(
0
)(1
0
00 >>
>
=
xxexx
xxxf xx
0x
20
-- III -
Y: III , Y=lnX, Y=logX X: - III X=eY . X=10Y
X(X=eY):
0,0,,)(ln
)(1
,0)(
0
)ln(
10
00 >>
>
=
xxexx
xxxf xx
6 21
- c2 -
X1,X2,,X N(0,1) ,
c2 . :
c2 c2 c2
222
21 ,..,, XXX
>
=
0,
)2(2
0,0
)( 22
12
xex
x
xfx
22
- -
F 1, 2
- 1, 2 ( ).
F :
2
22
1
21
=X
22
21,
>
+
=+ +
0,)()
2()
2(
)2
(
0,0
)( 221
2
1)121(1 )1(
2
2
1
21
21
x
x
xf xx
23
- (t) -
X: N(0, 1) , t t :
:
:
2
2Xt =
( ) ++
7 25
, , .
: , -, , 3, - 3.
2
Recommended