(27)
5. ³ : m =17; s=0,6. 䳿 (a<X<b); , (|-m| < d), a =16,8; b = 17,2; d=0,3.
г.
, (16,8; 17,2).
=
, m d
.
5 6 . .
', .
, , '.
( ) ' .
x1, x2, , xn...
, , . m1, m2, , mn...
, , .
. :
(28)
(29)
:
(30)
.
s = ÖD (31)
.
n .
` = , (33)
1/n - xi n , .
, (34)
, (33), n xi, , : :
(35)
(36)
:
(37)
(38)
mx* l. b , . b - , l,
P{| mx - mx*| < l} = b. (39)
, l,
a = 1 - b.
(39)
P{ (mx*- l) < mx < (mx* + l)} = b. (40)
г (40) , b mx L=[mx*- l, mx* + l].
, b L mx. b , L - .
|
|
6. s, ` , n. m b, s = 4; ` =15,6; = 64; b=0,95.
г.
(|`-m|<d) = b = 2*(d*Ö /s).
`-d<m<`+d.
2*(d*Ö /s)=0,95, (d*Ö /s)= 0,475. (d*Ö /s)=1,96;
, d=1,96*4 /Ö64=0,98.
m, b=0,95:
15,6-0,98 < m < 15,6+0,98,
14,62 < m < 16,58.
7.
x | |||||
mi |
, D, s .
г. , , :
s = ÖD
n - , n = S mi.
x ' = (x-a)/Dx,
mi; Dx - :
Dx = x+1 - x.
D :
.
:
` = `' * Dx + , D=D' * (Dx)2.
(m3 = 50) 3 = 20, 20; Dx =5, x ' = (x-20)/5.
i | mi | xi' | xi'*mi | (xi')2*mi |
-2 | -12 | |||
-1 | -16 | |||
S |
`' = 4 / 100 = 0,04, D'=80 / 100 - (0,04) 2= 0,798.
:
` = 0,04*5+20=20,2;
D =0,798*52=19,96;
s = Ö19,96 = 4,47.
7 .
.
Y
y = j(x) (41)
Y , j(x) - Y .
Y r:
y = rx + 2 (42)
r 2 , :
r = 1 = Kxy* / Dx*; 2 = `y a1` (43)
, (44)
, ' Y :
(45)
. X, Y. , .
, Y X
, (46)
:
n = Snx = Sny. (47)
(48)
; (49)
|
|
, (50)
Dx, Dy - ; a1, a2 - , :
n = Snx = Sny. (51)
(52)
; (53)
:
` = `' * Dx + a1, `y = `y' * Dy + a2. (54)
sx2 = sx'2 * (Dx)2; sy2 = sy'2 * (Dy)2; rb = rb'. (55)
8. 100 . . () (). y .
Y | ny | `xy | |||||
65,83 | |||||||
75,65 | |||||||
72,5 | |||||||
81,25 | |||||||
nx | |||||||
`yx | 12,5 | 21,43 | 29,23 | 29,28 |
г.
, a1 =70; a2 =25; D = 10; D= 5.
xi' yk' | -2 | -1 | n | n' | n'2 | nx'' | ||||
-3 | -12 | |||||||||
-2 | -16 | |||||||||
-1 | -12 | |||||||||
-1 | ||||||||||
n | ||||||||||
nxx' | -8 | -21 | S=25 | |||||||
nx'2 | S=119 | |||||||||
nx'' | S=81 | |||||||||
S= | S= | S= | ||||||||
`x' = 25/100 = 0,25; `y' = 16/100 = 0,16; sx'2 = 119/100 (0,25) 2 = 1,128;
sy'2 = 168/100 (0,16) 2 = 1,424;= 112.75; (x = 0,25*10+70 = 72,5;
`y = 0,16*5+25 = 25,8; sx2 = 1,128*102 = 112,8; sy2 = 1,424*52 = 35,6
rb' = rb = (0,81-0,25*0,16)/(Ö1,28 * Ö1,424) = 0,608.
:
`y 25,8 = 0,608 * (-72,5) *5,97/10,618;
`y = 0,342 + 1,03.
, :
= 60,
yx=60 = (2*10+4*15+5*20+6*25+4*30)/21 = 21,428,
yx=60 = 0,342*60 + 1,03 = 21,55; 0,122;
=80,
yx=80 = (25*10+10*30+6*35)/26 = 29,3,
yx=80 = 0,342 * 80 + 1,03 = 28,39; 0,84.