f(x)
0.5
0.3
0.2
0.1
V
....
....
........
,
,
,
I
t
0
2
4
6
8
10
x
f(x)
0.2
0.1
o
20
25
30
x
PHC. 3.48.
IlnOTHOCTb
BepOl'lTHOCTH x
2
-paClIpe,lleJIeHHl'I
ITHpcoHa.
238
K03<P<P
H
u,HeHT
V
x
=~
BapHau,HH
ACHMMeTPWI
Sk=j!
Ex
=
12
3KCu,ecc
n
HaqaJIbHhIe
m
2
=n(n + 2), m
3
=n(n + 2)(n + 4),
MOMeHTbI
m
4
=
n(n
+ 2)(n + 4)(n + 6),
s-I
m
s
=
n(n
+
2)
...
[n
+ 2(s
-1)]
=
IT
(n
+ 2k)
k=O
UeHTPaJIbHbIe
III =
8n,
114
=
12n
(n +
4)
MOMeHTbI
TOqKaMH
rrepern6a
<PYHKU,HH IIJIOTHOCTH
f(x)
HBJISIIOTCH
TOqKH
X = n - 2
=+=
,J2(n -
2)
(rrpH
yCJIOBHH, qTO X - ,ueHcTBHTeJIbHOe
rro-
JIO)lQITeJIbHOe qHCJIO).
COOTHoweHMR
MelKAY
pacnpeAeneHMRMM
1.
ECJIH
Ul>
U
2
,
...
,
Un
- He3aBHCHMhIe CTaH,llapTHhle
HOp-
MaJIbHble
cnyqaHHbIe
BeJI~HHhI,
TO
cnyqaHHaH
BeJIHqHHa
U;
+
ui
+ ... +
U;
HMeeT
X,
2_pacrrpe,ueJIeHHe C n CTerreHHMH CB060,ubI.
2. x,2_pacrrpe,ueJIeHHe C n CTerreHHMH CB060,ubI COBrra,uaeT C
raM-
Ma-pacrrpe,ueJIeHHeM
C
rrapaMeTPOM
MaCIIITa6a
A.
=
1/2
H
rrapaMeT-
pOM
<pOPMbI a =
n12.
3.
CnyqaHHaH
BeJI~HHa
X(n),
HMeIOlUaH x,2_pacrrpe,ueJIeHHe C n
CTerreIDIMH
cB060,ubI,
H CJIyqaHHaH
BeJI~HHa
Y(1, nI2),
HMeIOlUaH
raMMa-pacrrpe,ueJIeHHe
C
rrapaMeTPOM
MacIIITa6a
A.
= 1 H
rrapaMeT-
poM
<POPMbI a =
n12,
CBH3aHbI COOTHOIlleHHeM
X(n)
- 2Y(I, nI2).
4.
CyMMa
He3aBHCHMbIX CJIyqaHHbIX
BeJI~HH
Xl> X
2
,
...
, X
k
,
HMeIOIUHX
x,2_pacrrpe,ueJIeHHe C
nl>
n
2
,
...
, n
k
CTerreHHMH
cB060,ubI
COOTBeTCTBeHHO,
HMeeT
x,2_pacrrpe,ueJIeHHe C n =n
l
+ n
2
+...+ n
k
CTerreHHMH
cB060,ubI.
5.
He3aBHCHMble
CJIyqaHHbIe
BeJI~HHbI
X(n)
H
X(m),
HMeIO-
IUHe
x,2_pacrrpe,ueJIeHHe C n H m CTerreHHMH
cB060,ubI
COOTBeTCT-
BeHHO,
CBH3aHbI
co
CJIyqaHHoH
BeJIHqHHOH
F(n,m),
HMeIOlUeH
F-pacrrpe,ueJIeHHe
<1lHIllepa-CHe,ueKopa
C n H m CTerreHHMH
cB060-
,ubI, COOTHOIlleHHeM
x(n)/x(m)
=mX(n) _
F(n,m).
-n-
m
nX(m)
239