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??????? 1-3
??????? ?7
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?????? ???-III
?.?. ???????
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2012
??????? ? 1 ???? ??????: ???????????? ??????? ?? ?????????? ????????? ???????? ????????????? ??????????? ? ????? ?????????.
??????? ??????? ?7.
??? 10 ????????? ???????? "x" - ?????? ????????? ??? ?????? ??????? (???)
??????? ?1
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082?x10=26,593?2x10=3,98061
?????????? ??????? ?????????????? ???????? ??????????? 10 ????????? ?? ???????:
??? = - ????? ??????????? ?????? ?????????;
N - ?????????? ?????????.
x_(?? 10)=(2,407+2,216+...+2,483)/10=26,593/10=2,6593 ??? ?????????? ????????? ??????????? ??????????? ???? ????????? - "?"1,2...10,
??? ?1=X1-Xcp, ?2=X2-Xcp, ?N=XN-Xcp [??????? ?1].
????? ???????? ? ??????? ?????? ?? ?????????? ???????? "?"1,2...10. ????? ???? ????????? ??? ?????????? ???????? ?2 , ????????: ?2 X10 = 3,98061 [??????? ?1] ?????????? ??????? ?????????????? ?????????? ?????????? ?????????, ??????? ???????????? ????? ????????? ??????????? ??????????? ???? ????????? ?? ???????:
,
??? ?21=0,063655, ?22=0,196515, ?210=0,031082, ?210=3,98061
N - ?????????? ?????????.
s_[?] =v(3,98061/9)= 0,6650 ??? ?????????? ????????????? ???????? ??? ????? ????????? (10) ????????? ???????????? ?????????, ??????? ??????? ?? ???????? ???????????? ??????????? ? ????? ?????????. ??? 10 ????????? tC=1,83 ??? ????????????? ??????????? 0,9 (?? ??????? ?1 ???????????? ????????).
?????????? ????????? ???????? "X" ?? ?????????? ???????? ???? =0,6556 ? ?????????? ???????????? ????????? tC=1,83. ???????????? ?? ???????:
x_((0,9))=2,6593�1,83 0,6650/v10=(2,6593�0,3848) ??? ?????????????? ???????????? ???????? ????????????? ?????????? ??? ?????? ????????? ????????????? ???????????, ??????? ????????? ? ??????? ?1 ?.?., ? ?????? ??? ????????????? ??????????? 0,95 - ??????????? ????????? ????? 2,26, ??? 0,99 - tC ????? 3,25.
x_((0,95))=2,6593�2,26 (0,6650 )/v10=(2,6593�0,4753) ??? x_((0,99))=2,6593�3,25 0,6650/v10=(2,6593�0,6834) ??? ?????????? ??????????????? ???????????? ????????????? ????????? ??? 15 ? 20 ????????? ???????? ???????? "?".
??? ????????????? ??????? ?????? ? ??????? ?2 ? ?3 ??? ?????????????? 15 ? 20 ????????? ???????? "?".
??? 15 ????????? ???????? "?" - ?????? ????????? ??? ?????? ??????? (???)
??????? ?2
N ?/??, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,680,76610,586858123,7630,84910,720914131,926-0,98790,976012143,580,66610,443645154,1671,25311,570176?x10=43,709?2x10=8,92660
?????????? ??????? ?????????????? ???????? ??????????? 15 ????????? x_(?? 10)=2,9139 ??? ?????????? ??????? ?????????????? ?????????? ?????????? ?????????:
s_[?] =v(8,92660/14)=0,7985 ???
?????????? ????????????? ???????? ??? ????? ????????? (15) ????????? ???????????? ?????????, ??????? ??????? ?? ???????? ???????????? ??????????? ? ????? ?????????. ??? ????????????? ??????????? 0,95 - ??????????? ????????? ????? 2,15, ??? 0,99 - tC ????? 2,92. x_((0,95))=2,9139�2,15 (0,7985 )/v15=(2,9139�0,4433) ??? x_((0,99))=2,9139�2,92 (0,7985 )/v15=(2,9139�0,6020) ??? .
??? 20 ????????? ???????? "?" - ?????? ????????? ??? ?????? ???????.
??????? ?3
N ?/??, ?????x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x10=58,75?2x10=10,34924 x_(?? 10)=2,9375 ??? s_[?] =v(10,34924/9)=1,0723 ??? ?????????? ????????????? ???????? ??? ????? ????????? (15): x_((0,95))=2,9375�2,08 (1,0723 )/v20=(2,9375�0,4987) ??? x_((0,99))=2,9375�2,84 (1,0723 )/v20=(2,9375�0,6809) ??? ?????:
??? ?????????? ???????? ????????????? ???????????, ????????????? ???????? ???????????, ?? ???? ???????? ????????? ???????????.
??????? ? 2
???????? ?????? ????????????
???????? 3s
?????? ??????? ????????? ?????? ??? 3 ???????, ??? n=20.
N ?/???=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492 ????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/20* 58,750=2,9375 ???; s=v(1/19*10,3492)=0,7380 ??? ???? x_min<x_??-3s ? x_max>x_??+3s, ?? ???????? ????? ??????? ????????.
? �-3s=0,654
? �+3s=5,565
??? ???????? ?? ??????? ???????? ? ???????? (0,724; 5,152), ?????????????, ??? ?? ???????? ????????.
???????? ??????
???????: ???? | xi - x?? |>??* s[d]n - ?? ???????? ???????? ????????.
?? =(0,338+0,7144 ln n)/(1+0,0885 ln n)
????????? ??????? ??? 10 ????????? ???????? "x" - ?????? ????????? ??? ?????? ??????? (???)
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061???????? ???????? x4=3,884 ??? ? x5=1,401 ???.
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/10 26,593=2,659??? ; s_[d]10=v(1/9*3,98061)=0,6650 ???
????????? (???????????) ???????? ???????? ??????:
?_?=1,65 |x_????-X � | ?????????? ? s_[d]n K_?:
????????? 4-? ???????????? ????????? = 3,884 ??? .
??? ????? ???????? ??????????? ??????????? |x_????-X � |>s_[d]n K_?, ?.?. |3,884-2,659|>0,6650*1,65. ????? ???????, ??????????? ???????? 3,884 ???????? ???????? ? ?????????????.
????????? 5-? ???????????? ????????? = 1,401 ??? . ??? ????? ???????? ??????????? ??????????? |x_????-X � |>s_[d]n K_?, ?.?. |1,401-2,659|>0,6650*1,65. ????? ???????, ??????????? ???????? 1,401 ???????? ???????? ? ?????????????.
??? 15 ????????? ???????? "X" .
N ?/??, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660???????? ???????? x5=1,401 ??? ? x15=4,167 ???.
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/15* 43,709=2,914 ???; s_[d]15=v(1/14*8,92660)=0,7985 ???
?? =(0,3381+0,7144 ln n)/(1+0,0885 ln n)=1,83
????????? 5-? ???????????? ????????? = 1,401.
??? ????? ???????? ??????????? ??????????? |x_????-X � |>s_[d]n K_?, ?.?. |1,401 -2,914|>0,7985*1,83. ????? ???????, ??????????? ???????? 1,401 ???????? ???????? ? ?????????????.
????????? 15-? ???????????? ????????? = 4,167. ??? ????? ???????? ??????????? ??????????? |x_????-X � |>s_[d]n K_?, ?.?. |4,167-2,914|<0,7985*1,83. ????? ???????, ??????????? ???????? 4,167 ?? ???????? ????????.
??? 20 ????????? ???????? "?" .
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x8=1,401 ??? ? x18=4,167 ???.
X �=1/20 58,750=2,938 ???; s_[d]20=v(1/19*10,3492)=0,7380 ???
?_?=1,96
????????? 8-? ???????????? ????????? = 1,401 ???.
|1,401 -2,938|>0,7380*1,96. ????? ???????, ??????????? ???????? 1,401 ???????? ???????? ? ?????????????.
????????? 18-? ???????????? ????????? = 4,167 ???. |4,167 -2,938|<0,7380*1,96. ????? ???????, ??????????? ???????? 4,167 ?? ???????? ????????.
???????? ????????
???????: ???????? ??????? ??????? ?? ???? ??????? ????????? ?????????? x_i, ??? ??????? |ti=(xi- x??)/ s[d]n|> Zm,?.
z_(m,a)=(-1,4129344-0,21072302x+17,956435y-28,426808y^2)/(1-0,47529x+0,01145307x^3+11,034313y)
x=ln?(n); y=a
????????? ??????? ??? 10 ????????? ???????? "x"- ?????? ????????? ??? ?????? ??????? (???)
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061 ???????? ???????? x4=3,884 ??? ? x5=1,401 ???.
X �=1/10 26,593=2,659 ??? ; s_[d]10=v(1/9*3,98061)=0,6650 ???
????????? ??????????? ???????? ?? ???????, ????????? ????: ??? a=0,05 Zm,?=1,893
????????? ???????????? ????????:
t5 = (1,401 - 2,659)/ 0,6650=1,892
?.?. t5=1,892 < Zm,?=1,893 , ?? ???????? ?5=1,401 ??? ?? ???? ?? ?????????.
t8 = (3,884- 2,659)/ 0,6650=1,842
?.?. t5=1,842 <Zm,?=1,893 , ?? ???????? ?5=3,884 ??? ?? ???? ?? ???????????.
??? 15 ????????? ???????? "?".
N ?/??, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660???????? ???????? x5=1,401 ??? ? x15=4,167 ???
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/15 43,709=2,914 ???; s_[d]15=v(1/14*8,92660)=0,7985 ???
????????? ??????????? ???????? ?? ????? ????????? ???????
??? ?=0,05 Zm,?=1,923
????????? ???????????? ????????:
t5 = (1,401 - 2,914)/ 0,7985 =1,895. ?.?. t5=1,895 < Zm,?=1,923 , ?? ???????? ?5=1,401 ??? ?? ???? ?? ???????????.
t15 = (4,167- 2,914)/ 0,7985 =1,569. ?.?. t5=1,569 < Zm,?=1,923 , ?? ???????? ?5=4,167 ??? ?? ???? ?? ???????????.
??? 20 ????????? ???????? "?".
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x8=1,401 ??? ? x18=4,167 ???
X �=1/20 58,750=2,938 ???; s_[d]20=v(1/19*10,349)=0,7380 ???
????????? ??????????? ???????? ?? ????? ????????? ???????
??? ?=0,05 Zm,?=1,934
t8 = (1,401 - 2,938)/ 0,7380=2,083. ?.?. t5=2,083 > Zm,?=1,934 , ?? ???????? ?8=1,401 ??? ?? ???? ??????? ?????????.
t18 = (4,167- 2,938)/ 0,7380=1,665. ?.?. t5=1,665 < Zm,?=1,934 , ?? ???????? ?5=4,167 ??? ?? ???? ?? ???????????.
???????? ??????? - ????????
???????: ???????? ??? ?????? ?????????? 0,05 ? ??? n=10 ????????? ?? ??????? K_r (0,05;n)=1,2088-0.0033n+0.4965 ln?n-3,01/n
???? ?? >??(q, n), ?? ????????? ??????????? ??? ?????????? ?????? ??????
????????? ??????? ??? 10 ????????? ???????? "x" - ?????? ????????? ??? ?????? ??????? (???)
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061???????? ???????? x4=3,884 ??? ? x5=1,401 ???
X �=1/10 26,593=2,659 ??? ; s_[d]10=v(1/9*3,98061)=0,6650 ???
???????? ??? ?????? ?????????? 0,05 ? ??? n=10 ????????? ?? ???????
K_r (0,05;n)=1,2088-0.0033n+0.4965 ln?n-3,01/n
??? ?????? ?????????? 0,05 ??(q, n)=2,29
K_r4=|x_c-X � |/s_[d]10 =|3,884-2,659|/0,6650=1,842
K_r5=|x_c-X � |/s_[d]10 =|1,401-2,659|/0,6650=1,892
?????????? ???????? Kr ? Kr(q, n):
?? 4=1,842<??(q, n) =2,29 - ????????? ?? ???????? ???????.
?? 5=1,892<??(q, n) =2,29 - ????????? ?? ???????? ???????.
??? 15 ????????? ???????? "X".
N ?/??, ??? ??x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660???????? ???????? x5=1,401 ??? ? x15=4,167 ???.
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/15 43,709=2,914 ???; s_[d]15=v(1/14*8,92660)=0,7985 ???
??? ?????? ?????????? 0,05 ??(q, n)=2,30
??5 = |1,401 -2,914| / 0,7985=1,895
??5 =1,895<??(q, n) =2,30 - ????????? ?? ???????? ???????.
??15 = |4,167-2,914| / 0,7985=1,569
??15 =1,569<??(q, n) =2,30 - ????????? ?? ???????? ???????.
??? 20 ????????? ???????? "X".
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x8=1,401 ??? ? x18=4,167 ???.
X �=1/20 58,750=2,938 ???;? s?_[d]20=v(1/19*10,3492)=0,7380 ???
??? ?????? ?????????? 0,05 ??(q, n)=2,62
??8 = |1,401 -2,938|/ 0,7380=2,083
??8 =2,083<??(q, n) =2,62 - ????????? ?? ???????? ???????.
??18 = |4,167-2,938| / 0,7380=1,665
??18 =1,665<??(q, n) =2,62 - ????????? ?? ???????? ???????.
???????? ??????
???????: ?????????? ?????????? Z ?? ??????? Z=(Z_i-Z_??)/s
?? ??????? ??? Z ?????????? M
???? ?<n ??????, x_i ?? ???????? ????????.
????????? ??????? ??? 10 ????????? ???????? "x" - ?????? ????????? ??? ?????? ??????? (???)
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061???????? ???????? x4=3,884 ??? ? x5=1,401 ???
X �=1/10 26,593=2,6593 ???; s_[d]10=v(1/9*3,98061)=0,6650 ???
?????????? ?????????? Z ?? ??????? Z=|x_i-X � |/s
Z4 = |3,884 - 2,659|/ 0,6650=1,842
?? ??????? ?????????? M
??? Z=1,842 M=8
?.?. ?<n ??????, x4 ?? ???????? ????????.
Z5 = |1,401- 2,659|/ 0,6650=1,892
??? Z=1,892 M=9
?.?. ?<n ??????, x5 ?? ???????? ????????.
??? 15 ????????? ???????? "X".
N ?/? ?, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660???????? ???????? x5=1,401 ??? ? x15=4,167 ???
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/15 43,709=2,9139 ???; s_[d]15=v(1/14*8,92660)=0,7985 ???
Z 5= |1,401 - 2,914|/ 0,7985=1,895
?? ??????? ?????????? M
??? Z=1,842 M=8
?.?. ?<n ??????, x5 ?? ???????? ????????.
Z 15= |4,167-2,914| / 0,7985=1,569
??? Z=1,569 M=4
?.?. ?<n ??????, x15 ?? ???????? ????????.
??? 20 ????????? ???????? "X".
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x8=1,401 ??? ? x18=4,167 ???
X �=1/20* 58,750=2,9375 ???; s_[d]20=v(1/19*10,3492)=0,7380 ???
Z8 = |1,401 -2,938|/ 0,7380=2,083
?? ??????? ?????????? M ??? Z=2,083, M=13
?.?. ?<n ??????, x8 ?? ???????? ????????.
Z18 = |4,167-2,938| / 0,7380=1,665
?? ??????? ?????????? M ??? Z=1,665, M=5
?.?. ?<n ??????, x18 ?? ???????? ????????.
???????? ???????
???????: ???????? ??????? ???????????? ?? ???????:
?_?=(x_n-x_(n-1))/(x_n-x_1 )
???? ??(q,n)>??, ?? ????????? ?? ???????? ?????? ???????????.
????????? ??????? ??? 10 ????????? ???????? "x" - ?????? ????????? ??? ?????? ??????? (???)
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061???????? ???????? x4=3,884 ???
???????? ??????????? ????????? ??????????? ? ??????? ???????????:
1,401; 2,216; 2,407; 2,483; 2,483; 2,648; 2,685; 3,145; 3,241; 3,884.
??? ?????? ?????????? 0,05 ????????? (???????????) ???????? ???????? ??????? (??(q,n)) ?? ??????? ????? 0,41
????????? ???????? ???????? ??????? ?? ?? ???????
?_?=(x_n-x_(n-1))/(x_n-x_1 )=(3,884-3,241)/(3,884-1,401)=0,26
?.?. ??(q,n) =0,41>??=0,26 ????????? ?? ???????? ?????? ??????????? ? ???????????? ?=0,95
??? 15 ????????? ???????? "X".
N ?/??, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660???????? ???????? x15=4,167 ???
???????? ??????????? ????????? ??????????? ? ??????? ???????????:
1,401; 1,926; 2,216; 2,407; 2,483; 2,483; 2,648; 2,685; 3,145; 3,241; 3,580; 3,680; 3,763; 3,884; 4,167.
??? ?????? ?????????? 0,05 ????????? (???????????) ???????? ???????? ??????? (??(q,n)) ?? ??????? :
?_? (0,05;n)=v((-0,6691-0,0029n)/(1+n(-0,5605+0,00531n)))
?_? (0,05;n)=0,34 ??? n=15
????????? ???????? ???????? ??????? ?? ?? ???????
?_?=(x_n-x_(n-1))/(x_n-x_1 )=(4,167-3,884)/(4,167-1,401)=0,10
?.?. ??(q,n) =0,34>??=0,10 ????????? ?? ???????? ?????? ??????????? ? ???????????? ?=0,95
??? 20 ????????? ???????? "X".
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x18=4,167 ???
???????? ??????????? ????????? ??????????? ? ??????? ???????????:
1,401; 1,926; 2,148; 2,216; 2,407; 2,483; 2,483; 2,648; 2,685; 2,802; 2,979; 3,145; 3,241; 3,502; 3,580; 3,610; 3,680; 3,763; 3,884; 4,167.
??? ?????? ?????????? 0,05 ????????? (???????????) ???????? ???????? ??????? (??(q,n)) ?? ??????? ????? 0,3
????????? ???????? ???????? ??????? ?? ?? ???????
?_?=(x_n-x_(n-1))/(x_n-x_1 )=(4,167-3,884)/(4,167-1,401)=0,10
?.?. ??(q,n) =0,3>??=0,10 ????????? ?? ???????? ?????? ??????????? ? ???????????? ?=0,95
???????? �max ??? ????????? ?????? ???????????? ? ????????
???????: ?????????? ???????????? ?? ????????:
�_1=(x_max-X �)/(sv((n-1)/n)) ;�_2=(X �-x_min)/(sv((n-1)/n))
�1< �max ???????? xmax ?? ???????? ????????
�2> �min ???????? xmin ?? ???????? ????????
?? ??????? ?????????? �max ? ??????????? ?? n
????????? ??????? ??? 10 ????????? ???????? "x" - ?????? ????????? ??? ?????? ??????? (???)
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061???????? ???????? x4=3,884 ??? ? x5=1,401 ???
X �=1/10 26,593=2,6593??? ; s_[d]10=v(1/9*3,98061)=0,6650 ???
?????????? ????????????:
�1 = (3,884-2,659)/ 0,63=1,944
�2 = (2,659-1,401)/ 0,63=1,997
?? ??????? ?????????? �max= 2,29
�1=1,944< �max= 2,29 ???????? xmax ?? ???????? ????????
�2=1,997< �max= 2,29 ???????? xmin ????????? ??? ?????? ???????????
??? 15 ????????? ???????? "X".
N ?/??, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660???????? ???????? x5=1,401 ??? ? x15=4,167 ???
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/15* 43,709=2,9139 ???; s_[d]15=v(1/14*8,92660)=0,7985 ???
?????????? ????????????:
�1 = (4,167-2,914)/ 0,77=1,627
�2 = (2,914-1,401)/ 0,77=1,965
?? ??????? ?????????? �max= 2,49
�1=1,627< �max= 2,49 ???????? xmax ?? ???????? ????????
�2=1,965< �max= 2,49 ???????? xmin ????????? ??? ?????? ???????????
??? 20 ????????? ???????? "X".
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x8=1,401 ???; x16=1,926 ??? ? x18=4,167 ???
X �=1/20* 58,750=2,9375 ???; s_[d]20=v(1/19*10,3492)=0,7380 ???
?????????? ????????????:
�1 = (4,167-2,938)/ 0,72=1,707
�2 = (2,938-1,401)/ 0,72=2,135
?? ??????? ?????????? �max= 2,62
�1=1,707< �max= 2,62 ???????? xmax ?? ???????? ????????
�2=2,135< �max= 2,62 ???????? xmin ????????? ??? ?????? ???????????
???????? ????????????
???????: R???? = |xi-x??|/ s[d]i
???? R???? <R?? ????????? ?? ???????? ????????
?? ??????? ?????????? ??????????? R?? (q=0,05 ;n )
????????? ??????? ??? 10 ????????? ???????? "x" - ?????? ????????? ??? ?????? ??????? (???)
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061???????? ???????? x4=3,884 ??? ? x5=1,401 ???
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/10 26,593=2,6593 ???; s_[d]10=v(1/9*3,98061)=0,6650 ??? ???????? ????????? ???????? ???????? R???? ??? ??????? ????????:
R_????4=|x_i-X � |/s_x =|3,884-2,659|/0,665=1,842
???????? ????????? ???????? ???????? R???? ??? ??????? ????????:
R_????5=|x_i-X � |/s_x =|1,401-2,659|/0,665=1,892
????????? ??????????? ???????? ???????? ???????????? R?? =2,41:
??????? ???????? R???? ? R??(a,n):
R????4 =1,842<R?? =2,41- ????????? ?? ???????? ????????
R????5=1,892<R?? =2,41- ????????? ?? ???????? ????????
??? 15 ????????? ???????? "X".
N ?/??, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660 ???????? ???????? x5=1,401 ??? ? x15=4,167 ???
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/15* 43,709=2,9139 ???; s_[d]15=v(1/14*8,92660)=0,7985 ???
???????? ????????? ???????? ???????? R???? ??? ??????? ????????:
R_????5=|x_i-X � |/s=|1,401-2,914|/0,799=1,894 ???????? ????????? ???????? ???????? R???? ??? ??????? ????????:
R_????15=|x_i-X � |/s=|4,167-2,914|/0,799=1,568 ????????? ??????????? ???????? ???????? ???????????? R?? =2,64:
??????? ???????? R???? ? R??(a,n):
R????5 =1,894<R?? =2,64- ????????? ?? ???????? ????????
R????15 =1,568<R?? =2,64- ????????? ?? ???????? ????????
??? 20 ????????? ???????? "X".
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x8=1,401 ??? ? x18=4,167 ???
X �=1/20 58,750=2,9375 ???; s_?=v(1/19*10,3492)=0,7380 ???
???????? ????????? ???????? ???????? R???? ??? ??????? ????????:
R_????8=|1,401-2,938|/0,738=2,083
???????? ????????? ???????? ???????? R???? ??? ???????? ????????:
R_????18=|4,167-2,938|/0,738=1,665
????????? ??????????? ???????? ???????? ???????????? R?? =2,78:
R????8 =<R?? =2,78- ????????? ?? ???????? ????????
R????18 =<R?? =2,78- ????????? ?? ???????? ????????
???????? ?????????? ?????? ???????????? ? ???????? ??? ??????????? ????????? ??????????????? ???????? ? ????????? ??????????? ????????????
???????: ?????????? ???????????? W?_?? ?? ???????:
W_??=(0,6347823+0,77301434x-0,212556x^2+0,190149y):
:(1+0,096651668x+4,0385356*?10?^(-7)*x^2+0,20545356y+0,012637605y^2-2,5088*?10?^(-7)*y^3)
x=ln?n ; y=ln?q , ??? q=0,05
???? t>W??, ?? ???????? ???????? ????????.
????????? ??????? ??? 10 ????????? ???????? "x"
N ?/??, ????=x-x???2=(?-???)212,407-0,25230,06365522,216-0,44330,19651532,483-0,17630,03108243,8841,22471,49989051,401-1,25831,58331962,6850,02570,00066073,2410,58170,33837583,1450,48570,23590492,648-0,01130,000128102,483-0,17630,031082 ?x10=26,593 ??x10=3,98061???????? ???????? x4=3,884 ??? ? x5=1,401 ???
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/10 26,593=2,6593 ??? ; s_[d]10=v(1/9*3,98061)=0,6650 ???
W??=0,997
t=(x_max-? �)/s=(3,884-2,659)/0,6650=1,842
??? ??? t=1,842>W??=0,997, ?? ???????? ???????? ????????, ????????? ?? ???? ????????. ??? 15 ????????? ???????? "X".
N ?/??, ?????x-x???2=(?-???)212,407-0,50690,25698122,216-0,69790,48711132,483-0,43090,18570443,8840,97010,94102951,401-1,51292,28896762,685-0,22890,05241073,2410,32710,10697383,1450,23110,05339292,648-0,26590,070721102,483-0,43090,185704113,6800,76610,586858123,7630,84910,720914131,926-0,98790,976012143,5800,66610,443645154,1671,25311,570176?x15=43,709??x15=8,92660 ???????? ???????? x5=1,401 ??? ? x15=4,167 ???
????????? ??????? ???????? ? ?????????????????? ??????????:
X �=1/15* 43,709=2,9139 ???; s_[d]15=v(1/14*8,92660)=0,7985 ???
W??=0,789
t=(x_max-? �)/s=(4,167-2,914)/0,799=1,568
??? ??? t=1,568>W??=0,789, ?? ???????? ???????? ????????, ????????? ?? ???? ????????. ??? 20 ????????? ???????? "X".
N ?/??, ????=x-x???2=(?-???)213,5020,56450,31866022,9790,04150,00172232,802-0,13550,01836042,407-0,53050,28143052,216-0,72150,52056262,483-0,45450,20657073,8840,94650,89586281,401-1,53652,36083292,685-0,25250,063756103,2410,30350,092112113,1450,20750,043056122,648-0,28950,083810132,483-0,45450,206570143,6800,74250,551306153,7630,82550,681450161,926-1,01151,023132173,5800,64250,412806184,1671,22951,511670192,148-0,78950,623310203,6100,67250,452256?x20=58,75??x20=10,3492???????? ???????? x18=4,167 ???
X �=1/20* 58,750=2,9375 ???; s_?=v(1/19*10,3492)=0,7380 ???
W??=0,601
t=(x_max-? �)/s=(4,167-2,938)/0,738=1,665
??? ??? t=1,665>W??=0,601, ?? ???????? ???????? ????????, ????????? ?? ???? ????????. ????? : ???????????????????? ???????? ?????? ??????????????????? ???????? ?????? ??????????????????? ???????? ??????? ???????3,8841,4011,4014,1671,4014,1673s----???????? ?????? ? ?????????? ??????????????
???????????????????? ?????????????? ???????????????? ???????? ???????? ???????? ?????????????? ????????????? - ?????????? ???????? ???????? ???????? ???????? ???????? ?????????????? ???????? ???????? ???????? ???????? ???????? ??????????????? ??????--?? ??????-- ?? ??????�max?? ???????????????????? ????????????- ?? ??????????????-?????? ???????? ???????? ???????? ???????? ???????? ?????????????-??? ?????? ?????????-?????????--??????-??????
?? ?????? ??????? ????? ??? ???????????? ???????? ?? ??????? ??????? ?????? ? ????????????? ???????? ? ????????? ?? ????????. ???????????? ???????? ?? ?????? ? ?????? ??????? ??????????? ?????? ?????????????? ? ????? ?? ????????? ?????????
?? ???? ????????? ????? ???????? ?????????? ???? ???????? 3s, ?? ??? n<30 ?????????? ?????????? ? ???????? ??????????, ??????? ??? ?????? ? ?????? ??????? ????? ?? ?????????????. ??? ?? ???????? ?????? ?????????? ?????????? ??? ??????? ?? ???????? ???????????? ? ????????.
??????? ? 3 ???? ??????:
1.???????? ??????????????? ????????????? ???????? ?????????.
2. ??????????? ?????? ????????? ???????? ???????? ?????????.
???????? ?????????: ????? 40 ?????????? ????????? ?? ??????, ???????????? "Mahr", ????????.
????? ??????????????:
???????????? ????????????
???? ??????? 0,01 ??
??? ?????? ????? 0,5 ??
?????????????? ????????????? ???????????
???? ?????????? ?? ??????????? ???????????? ????? ?? ??????????? ?????????
????? ?????? ???????????
????????????????? ????????
????????????? ???????? ????
??????? ??????????? ?????????? ????????
????????
??????????? ??????????????
?????????????
????????, ?????????????,
????, ??b, ??c, ??d, ???, ??175-20072051131543,5 ?????? ????????? ???????? ????????? ??????????.
?????????? ??? ?????????? ?????? ?????? ??? ????????? ????? ???????? ??????? ? ????? ????????? ??????? ???????. ????? ????????? ????????? ? ?????????? ????, ??? ????? ?????? ????? ??? ???????? ???????? ? ???????????? ??????????????? ?????. ???? ??????? ?????????? ?????? ???? ????? ????????, ??? ????? ??? ????? ???????? ???????, ? ??????? ???? ?????? ?????, ? ?????? ??????. ????? ??????? ??? ????? ??????? ???????? ??? ?????????? ?????????? ???????????????? ?????????? ? ????????? ?????. ?????? ???????? ???????? ????? ????????? ?????? ????? ?? 0,01 ??.
??? ?? ??????????? ????? ?????????? ?? - ?? ??????????? ?????. ?? ??? ????? ??????? ?????????? ???????????? ?????, ???????????? ??????, ??????? ? ??????????? ??????? ????? ???????????? ?????????. ????? ????????????? ???????? ????????? ? ???, ????? ??????????????, ??? ???? ?????????? ???????? ? ?????????, ??????????????? ?????? ??? ????? ?????????? ?????.
??? ?????????? ???????? ??????? ? ????? ????????????? ?????? ??????????? ???? ????????????? ? ???????????? ????? ??? ???????????? ? ????????? ?????? ? ?????????? ???????? ??????; ??????????? ???? ???, ????? ?????? ???? ?? ????? ?? ???????????? ????. ???????? ?????? ????? ? ?????????? ?????????? ????? ??? ?? ????????? ??????????? ???????.
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