Tsu-2011 - ieeetsu

Tavi VI
normaluri ganawileba
SemTxveviT sidides ewodeba normaluri da aRiniSneba simboloTi
2
Na ( , ), Tu mis ganawilebis simkvrives (Sesabamisad, ganawilebis funqcias)
aqvs saxe:
2
( xa)
2
2
x
1
1
2
f 2 () x e (Sesabamisad,
2
2 ()
N( a, )
( , )
2
F x Na
2
e
dt
).
standartuli normaluri ganawilebis ( N (0,1) ) simkvrive (Sesabamisad,
ganawilebis funqcia) aRiniSneba simboloTi:
x
1
( x): f
2
N(0,1)
( x)
e (Sesabamisad,
2
2
2
2
( ta)
2
x t
1
( x): F
2
N(0,1)
( x)
e dt
2
; garda
x t
1
amisa, ixmareba aRniSvna:
2
0( x):
e dt
2
).
0
cxadia, rom: ( x) ( x)
; ( x) 1 ( x)
; ( x) 0.5
0( x)
, x 0 ;
2
N( a, ) a
N(0,1)
; P{ N(0,1) c, d} ( d) ( c)
;
2
a,
2
d a c a
2
x
a,
0.1 0.1 p
a
P{ N( a, ) c, d} ( ) ( ) ; xp
xp
a ; xp
, sadac
2
x
2
aris Na ( , )-is p -kvantili.
a,
p
Tu 0. 5, maSin 0(
z ) 0. 5
; xolo Tu 0. 5, maSin
0(
z
) 0.5 , sadac z standartuli normaluri ganawilebis zeda -
kritikuli wertilia.
magaliTebis amoxsnis nimuSebi:
magaliTi 1. vipovoT albaToba imisa, rom standartuli normaluri
SemTxveviTi sidide naklebia 1.18-ze, PN ( (0,1) 1.18) ?
amoxsna. davxazoT standartuli normaluri ganawilebis simkvrivis
wiri da abscisTa RerZze avRniSnoT 1.18-is Sesabamisi wertili (am SemTxvevaSi
z 1.18 ).
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