Tsu-2011 - ieeetsu

magaliTi 7. mowyobileba Sedgeba 10 damoukideblad momuSave elementisagan,
romelTagan TiToeulis mwyobridan gamosvlis albaToba T
droSi aris 0.05. SeafaseT albaToba imisa, rom T droSi mwyobridan gamosul
elementTa raodenobisa da elementebis mwyobridan gamosvlaTa sa-
Sualo ricxvs Soris gansxvavebis moduli aRmoCndeba: a). 2-ze naklebi; b).
2-ze aranaklebi.
amoxsna. a). aRvniSnoT S n
simboloTi T droSi mwyobridan gamosul
elementTa raodenoba. cxadia, rom am SemTxveviT sidides aqvs binomialuri
ganawileba da amitom:
ESn
np 100.05 0.5 da DSn
npq 10 0.05 0.95 0.475 .
visargebloT CebiSevis utolobiT. gvaqvs:
2
P(| Sn ESn | ) 1 DS
n
/ ,
P(| Sn
0.5| 2) 10.475/ 4 0.88 .
b). ramdenadac | Sn
0.5| 2 da | Sn
0.5| 2 sawinaaRmdego xdomilebebia,
amitom SegviZlia davweroT, rom:
P(| Sn
0.5| 2) 10.88 0.12 .
magaliTi 8. A xdomilebis moxdenis albaToba TiToeul eqsperimentSi
aris 0.5. SevafasoT albaToba imisa, rom 100 damoukidebel eqsperimentSi
A xdomilebis moxdenaTa S n
ricxvi moTavsebulia 40-dan 60-mde.
amoxsna. am SemTxvevaSi:
ESn
np 100 0.5 50 da DSn
npq 100 0.5 0.5 25 .
gasagebia, rom xdomileba 40 S n
60 eqvivalenturi xdomilebis:
40 50 S n
50 60 50 10 S n
50 10 | Sn
50| 10.
Sesabamisad, CebiSevis utolobis Tanaxmad SegviZlia davweroT,
rom:
P(40 Sn
60) P(| Sn50| 10) 125/100 0.75 .
magaliTi 9. rogor davadginoT albaToba imisa, rom SemTxveviT SeCeuli
adamiani agrovebs markebs? SeiZleba gamovkiTxoT garkveuli raodenoba
SemTxveviT SerCeuli adamianebis. Tu n gamokiTxulSi S
n
filatelistia, maSin saZiebeli albaToba p Sn / n. ramdeni adamiani unda
gamoikiTxos, rom cdomileba ar aRematebodes 0.005-s, Tu Cven gvinda, rom
swori Sedegi miviRoT albaTobiT 0.95?
amoxsna. amocanis pirobis Tanaxmad P(| S n
/ n p | 0.005) 0. 95. amitom
muavr-laplasis integraluri formula gvaZlevs:
0.95
P(|
S / n p | 0.005) P(
0.005
( S np)/
n 0.005)
n
n
n
n
n
P(
0.005
( Sn np)/
npq 0.005 ) (0.005
) (
0.005
).
pq
pq
pq
pq
amitom, Tu visargeblebT TanafardobiT ( x)
1(
x)
, miviRebT,
rom
n
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