Tsu-2011 - ieeetsu

amoxsna. SemoviRoT xdomilebebi: A { studentiSexvda i leqtors}
,
i 0,1,2,3 . maSin CvenTvis saintereso xdomileba iqneba Ai
. cxadia, rom
i
A 3 i
0
A
i
xdomilebebi wyvil-wyvilad uTavsebadia da Sesabamisad
P ( A)
P(
).
3 i0
amasTanave, TiToeuli A i
xdomilebis albaTobis gamosaTvlelad unda visargebloT
muavr-laplasis lokaluri formuliT. gvaqvs:
01200
0.002
P ( A0 ) P1200
(0) (
)/ 1200
0.002 0.998
0.0775 ;
1200
0.002 0.998
112000.002
P ( A1 ) P1200(1)
(
)/ 12000.0020.998
0.1719;
12000.0020.998
2 12000.002
P ( A2 ) P1200(2)
(
)/ 12000.0020.998
0.2505;
12000.0020.998
31200
0.002
P ( A3 ) P1200
(3) (
)/ 1200
0.002 0.998
0.2389 .
1200
0.002 0.998
amitom saZiebeli albaToba iqneba
P ( A)
0.0775
0.1719
0.2505
0.2389
0.7388.
magaliTi 5. rogoria albaToba imisa, rom wesieri monetis 200-jer
agdebisas gerbi mova aranakleb 95-jer da araumetes 105-jer?
amoxsna. unda visargebloT muavr-laplasis integraluri formuliT,
sadac n 200,
a 95, b 105,
p q 1/
2. gvaqvs:
105
2000.5
95
2000.5
P ( 95 S200
105)
(
) (
) (0.707)
(
0.707)
2000.5
0.5
2000.5
0.5
2(0.707)
1
20.761
0.52.
magaliTi 6. qarxnis nawarmis 4% mdare xarisxisaa. ramdeni nawarmi
unda SeirCes produqciis xarisxis Sesamowmeblad, rom albaTobiT 0.9 SegveZlos
imis mtkiceba, rom qarxnis nawarmis SemTxveviT SerCeul partia-
Si mdare xarisxis produqciis wilis gansxvaveba 4%-dan absoluturi sididiT
ar aRemateba 1%-s?
amoxsna. amocanis pirobis Tanaxmad , . iyos qarxnis
nawarmis SemTxveviT SerCeul partiaSi mdare xarisxis produqciis
wili. liapunovis Teoremis Tanaxmad SegviZlia vigulisxmoT, rom SemTxveviTi
sididis ganawileba axlosaa normalurTan da amitom
P {| 0.04|
0.01} 2(0.01/
)
1
0.9 .
aqedan ( 0.01/ )
0. 95da normaluri ganawilebis cxrilidan vpoulobT,
rom 0.01/
1.
65.
2
meores mxriv, p (1 p)/
n 0.040.96/
n anu 0.040.96/
n . Sesabamisad,
SegviZlia davweroT gantoleba
0.01/
0.040.96/
n 1.65,
saidanac advilad vipoviT, rom .
A i
88