Tsu-2011 - ieeetsu

n
n
2(0.005
) 1
0.95, anu ( 0.005 ) 0. 975.
pq
pq
saidanac standartuli normaluri ganawilebis funqciis cxrilis gamoyenebiT
vRebulobT, rom
n
0.005
1.96.
pq
Tuki axla gaviTvaliswinebT, rom pq 1/ 4 , advilad davaskvniT, rom
n 40.
magaliTi 10. mocemulia, rom P(| E | ) 0.8 da D 0.018 . ipoveT
.
2
amoxsna. CebiSevis utolobis Tanaxmad P(| E | ) 1 D / . maSasadame,
SegviZlia davweroT, rom
2
1 D/ 0.8 .
SevitanoT am gantolebaSi dispersiis mniSvneloba da amovxsnaT .
gvaqvs:
2
10.018/ 0.8 ,
aqedan, cxadia, rom 0.3 .
magaliTi 11. damoukidebel SemTxveviT sidideTa mimdevroba 1
, 2
,...
mocemulia ganawilebis kanoniT:
n
2
P
n 0 n
1/ 2n
2
1
1/ n
2
1/ 2n
akmayofilebs Tu ara es mimdevroba did ricxvTa kanons?
amoxsna. SevamowmoT CebiSevis Teoremis pirobebi. gasagebia, rom Sem-
TxveviTi sidideebi wyvil-wyvilad damoukidebelia. gamovTvaloT n
-is
maTematikuri lodini da dispersia. gvaqvs:
2 2 2
E n (1/2 n ) 0 (11/ n ) n
(1/2 n ) 0 ;
n
2 2 2 2 2 2 2 2 2 2 2 2
n
(1/2 ) 0 (1 1/ ) (1/2 ) (1/ )
2 2 2
D n
E n
( E n)
.
E n n n n n n n ;
amrigad, maTematikuri lodinebi sasrulia da dispersiebi Tanabrad
SemosazRrulia. amitom CebiSevis Teoremis Tanaxmad aRniSnuli mimdevroba
akmayofilebs did ricxvTa kanons.
amocanebi
1. vigulisxmoT, rom qalaqSi kacebisa da qalebis raodenoba erTidaigivea.
risi tolia albaToba imisa, rom 100 SemTxveviTi gamvlelidan 32 qali
iqneba?
2. cnobilia, rom detali wundebulia albaTobiT 0.6. ramden wundebul
detals unda velodoT 1000 detalidan albaTobiT 0.9?
90