Tsu-2011 - ieeetsu

Tavi II
ndobis intervali bernulis sqemaSi
ndobis intervali da SerCevis moculoba bernulis sqemisaTvis
(proporciisaTvis): bernulis sqemaSi ucnobi p albaTobis (populaciis
proporciis) wertilovani Sefasebaa fardobiTi sixSire w S / n, sadac
S
n
n
Xi
(
i
1
i1
X , Tu i -ur cdaSi moxda warmateba, da X 0, Tu i -ur cda-
Si moxda marcxi) – warmatebaTa raodenobaa n damoukidebel cdaSi.
mniSvnelovnebis donis mqone asimptoturi ndobis intervals ucnobi
p albaTobisaTvis (proporciisaTvis) aqvs Semdegi saxe:
wn (1 wn ) wn (1 wn
)
( wn z/2 , wn z/2
) .
n
n
populaciis proporciis l sizustis intervaluri SefasebisaTvis
saWiro SerCevis minimaluri moculobaa:
* z
/2 2
n [ wn(1 wn)( ) ] 1
l
(amasTanave, roca wn
-s aproqsimacia ucnobia, maSin unda gamoviyenoT
wn
0.5 , vinaidan namravlis wn(1 wn)
maqsimaluria, roca wn
0.5 ).
dazustebuli mniSvnelovnebis donis mqone asimptoturi ndobis
intervali ucnobi p albaTobisaTvis aris:
2 2 2 2
z /2
wn (1 wn ) z /2
z /2
wn (1 wn
) z
/2
wn z/2 w
2 n z/2
2
(
2n n 4n ,
2n n 4n
) .
2 2
z/2 z/2
1
1
n
n
mniSvnelovnebis donis mqone asimptoturi ndobis intervali puasonis
populaciis ucnobi parametrisaTvis aris:
X
n
X
n
( X
nz/2 , X
nz/2
) .
n
n
magaliTebis amoxsnis nimuSebi:
magaliTi 1. moxucebis 500 momvlelisagan Semdgar SerCevaSi 60 mamakacia.
ipoveT 90%-iani saimedoobis ndobis intervali moxucebis movlis
programaSi monawile mamakacTa WeSmariti proporciisaTvis.
amoxsna. vinaidan 10.90 0.10 , amitom z /2
z0.05 1.65 .
garda amisa, Sn
60 , n 500 . Sesabamisad, wn
60/500 0.12 da
1w n
10.12 0.88 .
amitom ndobis intervali iqneba:
i
n
n
104