Tsu-2011 - ieeetsu

magaliTi 7. benzingasamarTi sadguris yovelkvireuli moTxovna benzinze
gazomili 1000 litrebSi modelirdeba simkvrivis funqciiT:
f
() x 0,
sxvagan.
gamoTvaleT saSualokvireuli moTxovna benzinze.
amoxsna. ganmartebis Tanaxmad:
2
120 x (1 x), Tu 0 x 1;
1 1
2
3 4
0 0
4 5 1
(30x
24 x )|
030 24 6 .
E
xf ( x) dx x120 x (1 x) dx 120 ( x x ) dx
Sesabamisad, benzingasamarTi sadguris saSualo moTxovna benzinze
kviraSi Seadgens: 61000 6000 litrs.
magaliTi 8. uwyveti SemTxveviTi sididis ganawilebis simkvrivea:
3 x (2 x ), Tu 0 x 2;
f
() x 4
0, sxvagan.
ipoveT: a). saSualo; b). dispersia; g). P{ }
.
amoxsna. a).
b).
3 3 3
E
xf x dx x x x dx x x dx
2 2
2 3
( ) (2 ) ( )
0
4
0
2 4
3 4
x 3x
2
( )|
0 43 1;
2 16
2 2
2 2 2 2 3 2 3 3 3 4
D x f
( x) dx
x x(2 x) dx 1 ( x x ) dx 1
4 2 4
0 0
4 5
3x
3x
2 24 1
( )|
0
1 (6 ) 0 1 0.2
;
8 20 5 5
g). P{ } P{1 0.2
1 0.2}
3 3 3 3x
x
1
0.2 1
0.2 2 3
2 1
0.2
x(2 x) dx ( ) ( ) |
1 0.2
4 x x dx
2 4 4 4
1
0.2 1
0.2
2 3 2 3
3 (1 0.2) (1 0.2) 3 (1 0.2) (1 0.2)
( ) ( )
4 4 4 4
2 3 2 3
3 (1.447) (1.447) 3 (0.552) (0.552)
( ) ( ) 0.626 .
4 4 4 4
magaliTi 9. mocemulia ganawilebis simkvrive:
0, x 0,
f ( x) cos x, 0 x / 2,
0, x / 2.
ipoveT ganawilebis funqcia.
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