Tsu-2011 - ieeetsu
Tsu-2011 - ieeetsu
Tsu-2011 - ieeetsu
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E( | B) xiP( xi<br />
| B)<br />
.<br />
1<br />
cxadia, rom E( | ) E<br />
da E( | B) E( I )<br />
PB ( )<br />
B<br />
.<br />
SemTxveviTi sididis SemTxveviT sidideze regresiis mrudi<br />
(funqcia) ewodeba funqcias R( y) E( | y)<br />
.<br />
SemTxveviTi sidides R( ) (regresiis funqciaSi Casmulia SemTxveviTi<br />
sidide) SemTxveviTi sididis pirobiT maTematikur lodins uwodeben<br />
pirobiT da E( | ) simboloTi aRniSnaven.<br />
SemTxveviTi sididis dispersia.<br />
SemTxveviTi sididis dispersia D ganimarteba Semdegnairad:<br />
2 2 2<br />
DX E( E ) E ( E<br />
) .<br />
E -s ewodeba SemTxveviTi sididis meore rigis momenti (TviTon<br />
dispersias uwodeben agreTve – meore rigis centralur moments).<br />
Tu diskretuli tipis SemTxveviTi sididis ganawilebis kanonia<br />
x i x 1 x 2 x n<br />
p i p 1 p 2 p n<br />
maSin<br />
n n<br />
2<br />
(<br />
i<br />
<br />
j j)<br />
i<br />
i1 j1<br />
, anu<br />
DX x x p p<br />
36<br />
n<br />
i1<br />
n<br />
n<br />
2 2<br />
i i<br />
( j j)<br />
i1 j1<br />
.<br />
DX x p x p<br />
I. mudmivis dispersia nulis tolia -- Dc 0;<br />
2<br />
II. D( ab)<br />
a D<br />
.<br />
III. Tu da damoukidebeli SemTxveviTi sidideebia, maSin<br />
D( )<br />
D D<br />
.<br />
SemTxveviTi sididis pirobiTi dispersia B xdomilebis mimarT:<br />
2 2 2<br />
D( | B): E{[ E( | B)] | B} E( | B) [ E( | B)]<br />
.<br />
bernulis ganawilebas (anu bernulis SemTxveviT sidides) aqvs saxe:<br />
1 0<br />
P p 1<br />
p<br />
pda D p(1 p)<br />
.<br />
np da D np(1 p)<br />
.<br />
aq E<br />
binomialuri ganawilebis SemTxvevaSi: E<br />
hipergeometriuli ganawilebis SemTxvevaSi:<br />
nM <br />
nM ( N M) ( N n)<br />
E<br />
da D<br />
<br />
.<br />
2<br />
N<br />
N ( N1)<br />
puasonis ganawilebis SemTxvevaSi: E D .<br />
2<br />
geometriuli ganawilebis SemTxvevaSi: E 1/ p da D (1 p)/<br />
p .<br />
eqsponencialuri ganawileba. SemTxveviT sidides ewodeba eqsponencialurad<br />
ganawilebuli parametriT ( 0), Tu:<br />
0, x 0,<br />
f ( x)<br />
x<br />
e<br />
, x 0.<br />
2<br />
am SemTxvevaSi: E 1/ da D 1/ .
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