Tsu-2011 - ieeetsu

Tavi VII
albaTobis Teoriis zRvariTi Teoremebi
CebiSevis utoloba.
CebiSevis utoloba afasebs SemTxveviTi sididis gadaxras Tavisi
maTematikuri lodinidan. Tu raime SemTxveviTi sididea, maSin
nebismieri 0 ricxvisaTvis samarTliania utoloba:
2
P(| E | ) 1 D / .
did ricxvTa kanoni.
CebiSevis Teorema. vTqvaT, SemTxveviTi sidideebi 1,
2,...
wyvilwyvilad
damoukidebelia ( Ei
) da arsebobs iseTi ricxvi C , rom
D i
C, i 1,2,... . maSin nebismieri dadebiTi ricxvisaTvis sruldeba
utoloba:
1 2 n
E 1
E 2
E
n
lim P{| | } 1.
n
n
n
am mtkicebulebas did ricxvTa kanons uwodeben.
bernulis Teorema. davuSvaT, m aris n damoukidebel eqsperiment-
Si A xdomilebis moxdenaTa ricxvi, xolo p aris A xdomilebis
moxdenis albaToba calkeul eqsperimentSi. maSin nebismieri 0
ricxvisaTvis samarTliania utoloba
(1 )
{| m | }
p
P p
p ( 0 , roca n).
2
n
n
erTTan ragind axlos myofi albaTobiT SeiZleba vamtkicoT, rom
damoukidebel cdaTa sakmaod didi ricxvisaTvis dakvirvebadi xdomilebis
moxdenaTa sixSire ragind umniSvnelod gansxvavdeba misi moxdenis albaTobisagan
calkeul cdaSi.
centraluri zRvariTi Teorema.
did ricxvTa kanoni ar ikvlevs SemTxveviT sidideTa jamis ganawilebis
kanonis saxes. es sakiTxi Seiswavleba Teoremebis jgufSi, romlebsac
centraluri zRvariTi Teorema ewodeba. es Teorema amtkicebs, rom
SemTxveviT sidideTa jamis ganawilebis kanoni, romelTagan calkeul Sesakrebs
SeiZleba hqondes gansxvavebuli ganawileba, uaxlovdeba normalurs
SesakrebTa sakmaod didi ricxvis SemTxvevaSi. amiT aixsneba normaluri
ganawilebis kanonis uaRresad didi mniSvneloba praqtikul gamoyenebebSi.
Teorema 1. Tu 1
, 2
,... – damoukidebeli SemTxveviTi sidideebis mimdevrobaa,
erTi da igive ganawilebis kanoniT, maTematikuri lodiniT a da
dispersiiT σ 2 n
, maSin п –is usasrulod zrdisas S
jamis ganawilebis
kanoni uaxlovdeba standartul normalur ganawilebis kanons:
Sn
a
lim P{ x} ( x)
.
n
n
n
k1
k
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