ΜΑΘΗΜΑΤΙΚΑ ΚΑΙ ΣΤΟΙΧΕΙΑ ΣΤΑΤΙΣΤΙΚΗΣ ΛΥΣΕΙΣ...
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Transcript of ΜΑΘΗΜΑΤΙΚΑ ΚΑΙ ΣΤΟΙΧΕΙΑ ΣΤΑΤΙΣΤΙΚΗΣ ΛΥΣΕΙΣ...
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20 2015 :
1. )x(g)x(f)x(F .
))x(g)x(f())hx(g)hx(f()x(F)hx(F
))x(g)hx(g())x(f)hx(f( ,
0h , h
)x(g)hx(g
h
)x(f)hx(f
h
)x(F)hx(F
.
).x(g)x(fh
)x(g)hx(glim
h
)x(f)hx(flim
h
)x(F)hx(Flim
0h0h0h
)x(g)x(f))x(g)x(f(
2.
h
)x(f)hx(flim 00
0h
,
f 0x .
f x0, )( 0xf
f 0x . :
h
)x(f)hx(flim)x(f 000h
0
3. ()
21 x,...,x,x ,
(weighted
mean). xxx ,...,, 21 ,
-
()
21 w,...,w,w , :
1ii
1iii
21
2211
w
wx
w...ww
wx...wxwxx .
4. ) , ) , ) , ) ,)
1. 016813 2 xxx4
1x
3
1x
2
1x .
016813 2 xxx4
1x
3
1x
2
1x .
4
1 ,
3
1
2
1
2. 5
12
' ' ' ' ' '5 1 1
( )12 4 6
'' ' ' ' ' 1
1 1 1
1 1 1 1
3 2 6
' =1 - =4
3
3. ,
= + = + - 2 =4
1
4. 3
20239 2 xxx
3
1x 10
3
2
-
, :
=12
5+
3
2= 112
13 . ,
.
1. 1% 10%f 5% 30%f .
00 03
3 3 3 3 0
108360 360 0,3
360f f
3% 30%f
1 2 3 4 5 1f f f f f 3.042 ff (1)
5
1
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i
ii fxx 2 414 0,9 11 3,9 15 5,1f f
2 411 15 4,1f f (2). (1) (2) 1.02 f 2.04 f
2% 10%f 4% 20%f
2.
5 5i i2
i i
i 1 i 1
25
2i i5 5 _2 2 2 2 1
i i i i
i 1 i 1
x x s x x f ... 6,6
x 1
s x v x f x 202.6 14 6.6 v
57.26.62 ss
%10%35.1814
57.2_
x
sCV ,
3.
5 4
5 5_5 51 1
5 5
178014 14 14 14
1780 1780 178014 17 0,3 14 8,9 200
i i i i
i i
x v x v x vx v
xv v
x f
-
4.
a
i
aa
ii
s
aa
ss
aa__
1
: _
01
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aa s
a
s 1
1 a
a
ss
s
:
:
1 2 3 4 51 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
255 5
12 1 1
2
55
5 5
5 5 5 0
5 5
1
5 5 5
i
i i iii i
S
S S
SS
S
:
5
21
2
2
11
5
1 1
i SS
S S
1. ( = 90
) . . :
2222 100 x
100,100 2 xx
100,100)( 2 xxxABxf
2.
100,100
2100
2
2'
x
x
xxf
250' xxf
2500' xxf
10250' xxf 250 x f , 25x
.
x 0 5 2 10
f(x) + -
f(x)
-
255025100 2 ,
3.
x
xf
x 98
991lim
0
x
fxf
x 98
11lim
0 x 0
f 1 x f 11lim
98 x
99
99
99
98
98
11
98
1 ' f
2 2
0 0 0
2 2
0 2
2 2
0
1 100 1 991 99 1 99 2 99lim lim lim
98 98 98
1 99 2 99 1 99 2 99 lim
98 1 99 2 99
1 99 2 lim
x x x
x
x
x xf x x x x
x x x
x x x x x x
x x x x
x x x
2
2 2
0 2
2 4 3 3 2
0
99
98 1 99 2 99
2 1 99 2 99 lim
98 1 99 2 99
99 2 198 2 4 99 lim
x
x
x x x x
x x x x
x x x x
x x x x x x
2 2 99x x
2
0
98 1 99 2 99
limx
x x x x
x
3 2 299 2 198 2 4 2
98
x x x x x x
x
2
3 2 2
0 2
3 2 2
2
1 99 2 99
99 2 198 2 4 2 lim
98 1 99 2 99
99 0 0 2 0 198 2 0 4 0 0 2
98 0 1 99 0 2 0 99
x
x x x
x x x x x x
x x x
196 196
98 2 99
196
196
99
196
1 99.
9999 99
4. ABA 10 APBAP f
25,0
-
APfBAPf
BAP
APf
AP
BAPf
BAP
AP
AP
BAPAPAPBAPBAP
22
22
22
100100
1100100
0100100