TABELLENANHANG - Springer978-3-322-86263-1/1.pdf · N Tabelle 1: Binomialkoefflzienten
38
TABELLENANHANG 247
Transcript of TABELLENANHANG - Springer978-3-322-86263-1/1.pdf · N Tabelle 1: Binomialkoefflzienten
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8 9
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98
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99
9
---
-----
Anleitung zum Gebrauch der Tabelle 14
F(-y) = 1 - F(y)
Beispiele:
256
W(0,545 ~ X ~ 3,55) = F(3,55)- F(0,545)
0,9998 - 0,7071
0,2927
F(-2) 1 - F(2) = 1 - 0,9772
= 0,0228 .
Der 0,95-Punkt ist
YO,95 1,645.
I\)
VI ~
Tab
ell
a
14
: V
ert
el1
un
gsl
un
ktl
on
der
No
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ert
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g
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5010
10
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0
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a
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98
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0
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79
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5
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62
93
0
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31
0
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68
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91
0
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28
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b6
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71
10
0
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2
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1
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91
5
0.6
95
0
0.&
98
5
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01
9
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0,"
o
J.l0
88
~.7123
0 ••
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2'H
B
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2"
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aOO
--
Anleitung zum Gebrauch der Tabelle 15
Beispiele:
258
y
FUr n = 10 ergibt sich
W(7,5 ~ x ~ 30) = F(30) - F(7,5)
= 0,9991 - 0,3229
= 0,6762
Der 0,98-Punkt ist
YO , 98 = 21, 18 •
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N ~~;:~ _"'..o~CU U"II'","O" 0" U"0"1.1'V'U" 0"0'0'0'0" 0'f7'0'0' 0" 0'0'0"1.1'0"
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"""''''00 N .... _O,...
~:~~: NO''''.o,... ~ ....
~
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10101010 OO~IOC> OIOIDO~ """ ci~~~ "'0'-"'0' .o ... .o_r-- "'IO_~"" "''''''0'0' ..
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.oNII"\ __ CON ..... ,..ID ......
~ ~~g~ ::~:~ ~:~~:; 0""'''''''10 100"0"0"0" ::: CDCI'O'O' 0' 0"0"0"0"0" 0_"'''' "''O .... CDCC 0"0"0"0"0" 0"0"0"0"0" 0'0'0"0"0" ...... 10 lID 100 o lID 10 lID lID 10 lID 10 lID 10 1000100 0010100 IOIO~
• "'N'" NCCNo- ... ::!~~~ "'Nr--CI)G) NNCIONIII ~ .. '" '" .C_.., .0.00"-,(1 0",(10""'" ,..COCDO'O' ~gg ~ .. _COO"N II\ ........ 'ON ,..-..,"',.. "'''0''0''0'' 0'0"0"0'0-1010_'" "';~"'!":~ GO 0"0-0"0" 0"0"0"0"0- 0'0'0'0"0' "''''''' '" 10101010 IOCIIDIOC lID 1010 CO 101010100 10 0 'OC)IIO """
.;
NN'ON 10,.,_ .... .., ........ 0" CO 10000..oDCU .... NII'I,.,O" NII'I .... «I 0- "'''' ~
",0"''0 1010 .... ,.. .... __ "' .... GO
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Anleitung zum Gebrauch der Tabellen 16 und 17
YO,95
I f(TJ)dTJ 0,95
YO,95
Beispiel:
Der 0,95-Punkt der F(20;3)-Verteilung ist
YO,95 = 8,66 •
YO,99 I f(,,)dTJ = 0,99
YO,99 TJ
Beispiel:
Der O,99-Punkt der F(20;3)-Verteilung ist
YO,99 = 26,69 •
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Anleitung zum Gebrauch der Tabelle 18
y
F(-y) = 1 - F(y)
Beispiele:
FUr n ~ 10 ergibt sich
W(1,72 ~ X ~ 5,1) F(5,1) - F(1,72)
0,9998 - 0,9418
0,0580
F(-2) 1 - F(2) = 1 - 0,9633
0,0367 .
Der 0,99-Punkt ist
YO,99 = 2,767 .
267
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Tabelle 19: Zufallszahlen
0860 5519 1939 8116 0991 9786 9758 3776 7625 1585 3044 8087 0127 0894 2392 2569 8907 4043 6276 0755 4033 2796 8740 3235 9617 121+3 1223 2534 6333 9020
5516 6582 7616 3072 0151 2054 8431 5984 6421 9357 3051 9973 1021 7640 8337 8275 2941 1818 4304 0657 3742 2362 0940 5322 5584 1821 8813 2212 5432 5439
2440 8985 3726 6645 7369 5143 7735 2336 4477 6899 6215 6416 8608 9179 0303 3754 2432 8201 6041 0793 1974 4954 8473 9405 0233 9654 9178 9089 8606 0576
4458 5724 7507 31+76 2069 2575 4682 2721 2772 8768 2671 0866 4482 5714 6568 2108 8128 0886 8851 8928 9528 4104 9062 5963 7603 2635 9603 1+139 6325 8571
6098 5819 9219 2608 901+3 4627 3339 231+6 7196 2984 7711 6074 9624 4251 5655 5650 2917 1861 8166 4148 6827 4526 0660 31+17 6480 0694 9/+82 5781 5988 8625
2184 2252 4218 3014 6045 9145 2524 1740 5158 7776 4958 1370 4535 7642 9238 2115 2684 8767 3132 2454 2314 5148 5001 4253 1831+ 4623 5699 3598 5769 2164
271
Tabelle 20: Logarithmen
X LOGX X LOGX X LOG X X LOGX
1. 0000 I 0.0 1.6000 I 0.2041 2.2000 I 0.3424 2.8000 I 0.4472 1.0100 I 0.0043 1.1)100 I 0.201)8 2.2100 0.3444 2.8100 I 0.4487 1.0200 I 0.0086 1.1)200 I 0.2095 2.2200 0.3464 2.8200 I 0.4502 1. 0300 I 0.0128 1.1)300 I 0.2122 2.2300 0.3483 2.8300 I 0.4518 1.0400 I 0.0170 1.1)400 I 0.2148 2.2400 0.3502 2.8400 I 0.4533 1.0500 I 0.0212 1.6500 I 0.2175 2.2500 0.3522 2.8500 I 0.4548 1.01)00 I 0.0253 1.61)00 I 0.2201 2.21)00 0.3541 2.8600 I 0.4%4 1.0700 I 0.0294 1.6700 I 0.2227 2.2700 0.351)0 2.8700 I 0.4579 1. 0800 I 0.0334 1.1)800 I 0.2253 2.2800 0.3579 2.8800 I 0.4594 1.0900 I 0.0374 1.1)900 I 0.2279 2.2900 0.3598 2.8900 I 0.41)09
1.1000 I 0.0414 1.7000 I 0.2304 2.3000 0.3617 2.9000 I 0.41)24 1.1100 I 0.0453 1. 7100 I 0.2330 2.3100 0.31)31) 2.9100 I 0.41)39 1.1200 I 0.0492 1.7200 I 0.2355 2.3200 0.31)55 2.9200 I 0.41)54 1.1300 I 0.0531 1.7300 I 0.2380 2.3300 0.3674 2.9300 I 0.4669 1.1400 I 0.0569 1. 7400 I 0.2405 2.3400 0.3692 2.9400 I 0.4683 1.1500 I 0.0607 1.7500 I 0.2430 2.3500 0.3711 2.9500 I 0.41)98 1.11)00 I 0.0645 1.71)00 I 0.2455 2.3600 0.3729 2.91)00 0.4713 1.1700 I 0.01)82 1.7700 I 0.2480 2.3700 0.3747 2.9700 0.4728 1.1800 I 0.0719 1.7800 I 0.2504 2.3800 0.3761) 2.9800 0.4742 1.1900 I 0.0755 1.7900 I 0.2529 2.3900 0.3784 2.9900 0.4757
1.2000 I 0.0792 1.8000 I 0.2553 2.4000 0.3802 :;.0000 0.4771 1.2100 I 0.0828 1.8100 I 0.2577 2.4100 0.3820 3.0100 0.4781) 1.2200 I 0.0864 1.8200 I 0.2601 2.4200 0.3838 3.0200 0.4800 1.2300 I 0.0899 1.8300 I 0.2625 2.4300 0.3856 3.0300 0.4814 1. 2400 I 0.0934 1.8400 I 0.21)48 2.4400 0.3874 3.0400 0.4829 1.2500 I 0.0969 1.8500 I 0.2672 2.4500 0.3892 3.0500 0.4843 1.2600 I 0.1004 1.81)00 I 0.2695 2.4600 0.3909 3.0600 0.4857 1.2700 I 0.1038 1.8700 I 0.2718 2.4700 0.3927 3.0700 0.4871 1.2800 I 0.1072 1.8800 I 0.2742 2.4800 0.3945 3.0800 0.4886 1.2900 I 0.1106 1.8900 I 0.2765 2.4900 0.3962 3.0900 0.4900
1.3000 I 0.1139 1.9000 0.2788 2.5000 0.3979 3.1000 0.4914 1.3100 I 0.1173 1.9100 0.2810 2.5100 0.3997 3.1100 I 0.4928 1.3200 I 0.1201) 1.9200 0.2833 2.5200 0.4014 3.1200 I 0.4942 1. 3300 I 0.1239 1.9300 0.2856 2.5300 I 0.4031 3.1300 I 0.4955 1.3400 I 0.1271 1.9400 0.2878 2.5400 I 0.4048 3.1400 I 0.491)9 1. 3500 I 0.1303 1.9500 0.2900 2.5500 I 0.4065 3.1500 I 0.4983 1.3600 0.1335 1.9600 0.2923 2.5600 I 0.4082 3.1600 I 0.4997 1.3700 0.1367 1.9700 0.2945 2.5700 I 0.4099 3.1700 I 0.5011 1.3800 0.1399 1.9800 0.2967 2.5800 I 0.4111) 3.1800 I 0.5024 1.3900 0.1430 1.9900 0.2989 2.5900 I 0.4133 3.1900 I 0.5038
1.4000 0.1461 2.0000 0.3010 2.6000 I 0.4150 3.2000 I 0.5051 1. 4100 0.1492 2.0100 0.3032 2.6100 I 0.4166 3.2100 I 0.5065 1.4200 0.1523 2.0200 0.3054 2.6200 I 0.4183 3.2200 I 0.5079 1.4300 0.1553 2.0300 0.3075 2.6300 I 0.4200 3.2300 I 0.5092 1.4400 0.1584 2.0400 0.3096 2.6400 I 0.4216 3.2400 I 0.5105 1.4500 0.1614 2.0500 0.3118 2.6500 I 0.4232 3.2500 I 0.5119 1.4600 0.1644 2.0600 0.3139 2.6600 I 0.4249 3.2600 I 0.5132 1.4700 0.1673 2.0700 0.3160 2.6700 0.4265 3.2700 I 0.5145 1.4800 0.1703 2.0800 0.3181 2.1)800 0.4281 3.2800 I 0.5159 1.4900 0.1732 2.0900 0.3201 2.6900 0.4298 3.2900 I 0.5172
1.5000 I 0.1761 2.1000 I 0.3222 2.7000 0.4314 3.3000 I 0.5185 1.5100 I 0.1790 2.1100 I 0.3243 2.7100 0.4330 3.3100 I 0.5198 1.5200 I 0.1818 2.1200 I 0.3263 2.7200 0.4346 3.3200 I 0.5211 1. 5300 I 0.1847 2.1300 I 0.3284 2.7300 0.4362 3.3300 I 0.5224 1.5400 I 0.1875 2.1400 I 0.3304 2.7400 0.4378 3.3400 I 0.5237 1.5500 I 0.1903 2.1500 I 0.3324 2.7500 0.4393 3.3500 I 0.5250 1.5600 I 0.1931 2.1600 I 0.3345 2.7600 0.4409 3.3600 I 0.5263 1. 5700 I 0.195' 2.1700 I 0.3365 2.7700 0.4425 3.3700 I 0.5271) 1.5800 I 0.1987 2.1800 I 0.3385 2.7800 0.4440 3.3800 I 0.5289 1.5900 I 0.2014 2.1900 I 0.3404 2.7900 0.4456 3.3900 I 0.5302
272
Fortsetzung Tabelle 20
X LOGX X LOGX X LOGX X LOGX
3.4000 I 0.5315 4.0100 I 0.1)031 4.fi100 I o. fiFo 37 5.::'100 I 0.71fi8 3.4100 I 0.53?8 4.0?00 I 0.604::> 4.fi?00 I 0.6(,46 5.::>200 I 0.7177 3.4200 I 0.5340 4.0300 I 0.fi053 4. fi300 I 0.fi(,56 5.2300 I 0.7185 3.4300 I 0.5353 4.0400 I 0.6064 4.1)400 I 0.(,1)65 5.?400 I 0.7193 3.4400 I 0.5366 4.0500 I 0.6075 4.fi500 I 0.fi(,75 5.?500 I 0.7?0? 3.4500 I 0.5378 4.0(,00 I 0.(,085 4.fi('00 I 0.fi"84 5.?lioo I 0.7?10 3.4lioo I 0.5391 4.0700 I 0.(,096 4.li700 I 0.('li93 5.~'700 I 0.7':'18 3.4700 I 0.5403 4.0800 I 0.li107 4.6800 I 0.670? 5.::>800 I 0.7??6 3.4800 I 0.51.1" 4.0900 I o. (,117 4.6900 I 0.(;712 5.2900 I 0.7?35 3.4900 I 0.5428 4.1000 I 0.(;1?8 4.7000 I 0.1)7?1 5.3000 I 0.7?43
3.5000 0.51.41 4.1100 I oJ,138 4.7100 I 0.(,730 5.3100 I 0.7?51 3.5100 0.5453 4.1200 I 0.1';149 4.7200 I 0.1'-739 5.3?00 I 0.7'?59 3.5200 0.54,,5 4.1300 I o. ('1('0 4.1300 I 0.(;749 5.3300 I 0.7':'(7 3:5300 0.5478 4.1400 I 0.,,170 4.7400 I 0.li758 5.3400 I o.7?75 3.5400 0.5490 4.1500 I 0.6180 4.7500 I o. (,7(,7 5.3500 I 0.7?84 3.5500 0.550? 4.1600 I 0.(,191 4.7600 I 0.677" 5.31)00 I 0.n9? 3.5"00 0.5514 4.1700 I 0.li201 4.7700 I 0.(,785 5.3700 I 0.7100 3.5700 0.55?7 4.1800 I 0."?12 4.7800 I 0.li7Q4 5.3800 I 0.7,08 3.5800 0.5539 4.1900 I 0."?2? 4.7900 I 0.(,803 5.3900 I 0.7111i 3.5900 0.5551 4.?000 I o. (,?32 4.8000 I o. (,Al? 5.4000 I 0.71?4
3.1)000 0.5563 4.2100 I 0.(,?43 4.8100 I 0.1i821 5.4100 I 0.713? 3.6100 0.5575 4.?200 I 0.6253 4.8200 I 0.hA30 5.4200 I 0.7340 3.6200 0.5587 4.2300 I 0.621i3 4.8300 I o. li839 5.4300 I 0.7148 3.6300 I 0.5599 4.?400 I 0.fi274 4.8400 I 0.6848 5.4400 I 0.7351i 3.fi400 I 0.51ill 4.2500 I 0."?84 4.8500 I 0.1)857 5.4500 I 0.731)4 3.1)500 I 0.56?3 4.21)00 I 0.6?94 4.81)00 I 0.1)861) 5.41)00 I 0.737? 3.li600 I 0.5635 4.2700 I 0.6304 4.8700 I 0.li8r5 5.4700 I 0.7380 3.6700 I 0.5647 4.::>800 I 0.1)314 4.8800 I 0.li884 5.4800 I 0.7388 3.6800 I 0.51)58 4.2900 I 0.6325 4.8900 I 0.6893 5.4900 I 0.71Q6 3.1)900 I 0.5(,70 4.3000 I 0.6335 4.9000 I 0.1)90? 5.5000 I 0.7404
3.7000 I 0.568? 4.3100 I 0.6345 4.9100 I 0.1)911 5.5100 I 0.7412 3.7100 I 0.5694 4.3200 I 0.6355 4.9200 I 0.1';920 5.5200 I 0.7419 3.7200 I 0.5705 4.3300 I 0.6365 4.9300 I 0.6928 5.5300 I 0.74?7 3.7300 I 0.5717 4.3400 I 0.6375 4.9400 I 0.6937 5.5400 I 0.7435 3.7400 I 0.57?9 4.3500 I 0.1)385 4.9500 0.6946 5.5500 I 0.7443 3.7500 I 0.5740 4.3600 I 0.6395 4.91ioo 0.6955 5.51ioo I 0.7451 3.7600 I 0.5752 4.3700 I 0.li405 4.9700 0.1i91i4 5.5700 I 0.7459 3.7700 I 0.5763 4.3800 I 0.6415 4.9800 0.1i97? 5.5800 I 0.74('1i 3.7800 I 0.5775 4.3900 I 0.6425 4.9900 0.(,981 5.5900 I 0.7474 3.7900 I 0.5781i 4.4000 I 0.1)435 5.0000 0.(,990 5.1)000 I 0.748?
3.8000 I 0.5798 4.4100 I 0.6444 5.0100 0.6998 5.6100 I 0.7490 3.8100 I 0.5809 4.4200 I 0.1i454 5.0200 0.7007 5.6200 I 0.74Q7 3.8200 I 0.5821 4.4300 I 0.64li4 5.0300 0.7011i 5.6300 I 0.7505 3.8300 I 0.5832 4.4400 I 0.li474 5.0400 0.7024 5.li400 I 0.7513 3.8400 I 0.5843 4.4500 I 0.(,484 5.0500 0.7033 5.6500 I 0.75?0 3.8500 I 0.5855 4.4600 I 0.6493 5.olioo 0.7042 5.6lioo I 0.7528 3.8600 I 0.5866 4.4700 I 0.6503 5.0700 0.7050 5.6700 I 0.7531i 3.8700 I 0.5877 4.4800 I 0.6513 5.0800 0.7059 5.6800 I 0.7543 3.8800 I 0.5888 4.4900 I 0.li522 5.0900 0.70li7 5.li900 I 0.7551 3.8900 I 0.5899 4.5000 I o. li532 5.1000 0.7076 5.7000 I 0.7559
3.9000 I 0.5911 4.5100 I 0.6542 5.1100 0.7084 5.7100 I 0.7561) 3.9100 I 0.5922 4.5200 I 0.6551 5.1200 0.7093 5.7200 I 0.7574 3.9200 I 0.5933 4.5'300 I 0.6561 5.1300 0.7101 5.7300 I 0.7582 3.9300 I 0.5944 4.5400 I 0.6571 5.1400 0.7110 5.7400 I 0.7589 3.9400 I 0.5955 4.5500 I 0.6580 5.1500 I 0.7118 5.7500 I 0.7597 3.9500 I 0.5966 4.5600 I 0.6590 5.1600 I 0.7126 5.7600 I 0.7604 3.9600 I 0.5977 4.5700 I 0.6599 5.1700 I 0.7135 5.7700 I 0.761::> 3.9700 I 0.5988 4.5800 I 0.6609 5.1800 I 0.7143 'i.7800 I 0.7619 3.9800 I 0.5999 4.5900 I 0.6618 5.1900 I 0.7152 5.7900 I 0.7627 3.9900 I 0.1';010 4.6000 I 0.66::>8 5.2000 I 0.7160 5.8000 I 0.7634
273
Fortsetzung Tabelle 20
X LOGX X LOGX X LOGX X LOGX
5.Aloo I 0.7(,42 (,.4100 I 0.Ao(,9 7.0100 I 0.8457 7.(,100 I 0.8814 5.A200 I 0.7(,49 (,.4200 I 0.A075 7.0200 I 0.A4('3 7.(,200 I 0.B820 5.fl300 I 0.7('57 (,.4300 I 0.AoA2 7.0300 I 0.8470 7.6300 I 0.8825 5.A400 I 0.7(,64 6.4400 I 0.AoA9 7.0400 I 0.A476 7.6400 I 0.8831 5.fl500 I 0.7672 6.4500 I 0.A096 7.0500 I 0.fl482 7.(,Soo I 0.8837 5.A600 I 0.7(,79 (,.4600 I o.Alo? 7.0600 I 0.848A 7.6600 I 0.A842 5.A700 I 0.7(,8(, (,.4700 I 0.El109 7.0700 I 0.A494 7.6700 I 0.884A S.AAoo I 0.7(,94 (,.4Aoo I o.A11(, 7.oAoo I 0.8500 7.G800 I 0.8AS4 5.A900 I 0.7701 (,.4900 I 0.A12? 7.0900 I 0.8506 7.(,900 I 0.AA59 5.9000 I 0.7709 (,.5000 I 0.fll?9 7.1000 I 0.8513 7.7000 I 0.AAG5
5.9100 I 0.771G tl.51oo I 0.fl136 7.1100 I 0.851'1 7.7100 I 0.8A71 5.'1900 I 0.77?3 (,.5?00 I 0.fl142 7.1200 I 0.R5?5 7.7200 I 0.887G 5.9300 I 0.7731 (,.5300 I 0.8149 7.1300 I o. A5 31 7.7300 I 0.ABA2 5.9400 I o.773A (,.5400 I 0.fl156 7.1400 I 0.8537 7.7400 I 0.A8A7 5.9500 I 0.7745 G.5500 I o.Al('? 7.1500 I 0.A543 7.7500 I 0.8893 5.9(,00 I 0.7752 (,.%00 I 0.A169 7.1600 I 0.8549 7.7(,00 I 0.A899 5.9700 I 0.77(,0 (,.5700 I o.A17(, 7.1700 I 0.A555 7.7700 I 0.8904 5.9Aoo I 0.77(,7 (,.SAoo I 0.AIR2 7.1800 I 0.85(,1 7.7Aoo I 0.A910 5.9900 I 0.7774 (,.5900 I 0.AIA9 7.1900 I 0.A567 7.7900 I 0.8915 G.oooo I o.77A? (,.(,000 I 0.A195 7.2000 I 0.A573 7.Aooo I 0.A921
G.oloo I o.77A9 (,.6100 I 0.A202 7.2100 I 0.A579 7.Aloo I 0.A927 (,.0200 I 0.779G (,.(,200 I 0.A209 7.2200 I 0.A5A5 7.A200 0.A93? (,.0300 I 0.7A03 (,.G300 I 0.fl?15 7.2300 I 0.A591 7.fl3oo 0.A93A (,.0400 I 0.7A10 G.(,400 0.A22? 7.2400 I 0.A597 7.8400 0.fl943 (,.0500 I 0.7fl1A (,.6500 0.fl?28 7.2500 I 0.8603 7.flSoo 0.A949 6.0(,00 I 0.7A?5 G.6Goo 0.8235 7.2600 I 0.8G09 7.A600 0.8954 (,.0700 I 0.7R32 6.(,700 0.fl241 7.2700 I 0.8615 7.A700 0.8960 ('.oAoo I 0.7A39 (,.6Aoo 0.A24fl 7.2Aoo I 0.A621 7.A800 0.8965 (,.0900 I 0.7A46 6.(,900 0.A254 7.2900 I 0.A627 7.A900 0.A971 6.1000 I 0.7fl53 ii.7000 0.A2(,1 7.3000 I 0.A(,33 7.9000 0.A97('
(,.1100 I 0.7A(,0 6.7100 0.A2(,7 7.3100 I 0.8639 7.9100 0.89A2 (,.1200 I 0.7fl(,fl (,.7200 0.A274 7.3200 I 0.A645 7.9200 0.A9A7 (,.1300 I 0.7A75 (,.7300 0.A2Ao 7.3300 I 0.86S1 7.9300 0.A993 6.1400 I 0.7AA? (,.7400 0.fl2fl7 7.3400 I 0.8657 7.9400 0.A99A (,.lSoo I 0.7flA9 6.7500 0.A293 7.3500 I 0.B663 7.9500 0.9004 (,.1600 I o.7A9(, (,.7(,00 0.8299 7.3600 I 0.A669 7.9600 I 0.9009 (,.1700 I 0.7903 (,.7700 0.A30(, 7.3700 I 0.8675 7.9700 I 0.9015 (,.lAoo I 0.7910 (,.7Aoo 0.A312 7.3800 I 0.A681 7.9Boo I 0.9020 (,.1900 I 0.7917 (,.7900 0.A319 7.3900 I 0.A68(, 7.9900 I 0.9025 6.2000 I 0.7924 6.flooo o. A325 7.4000 I 0.fl(,92 A.oooo I 0.9031
(,.2100 I 0.7931 (,.A100 I 0.8331 7.4100 I 0.fl69R 8.0100 I 0.903(' (,.2200 I 0.793A 6.<1200 I 0.fl33A 7.4?00 I 0.8704 A.0200 I 0.9042 (,.2300 I 0.7945 (,.A300 I 0.fl344 7.4300 I 0.A710 A.0300 I 0.9047 ('.?400 I 0.7952 6.A400 I 0.A351 7.4400 I 0.A716 A.0400 I 0.9053 (,.?500 I 0.7959 (,.A500 I o .A357 7.4500 I 0.8722 A.0500 I 0.9058 6.2600 I 0.7966 6.A600 I 0.A)!)3 7.4600 I 0.A727 A.o(,oo I 0.90(,3 ii.2700 I 0.7973 (,.A700 I 0.A37o 7.4700 I 0.8733 A.0700 I 0.90(,9 (,.2Aoo I 0.79Ao (,.AAoo I 0.A37(, 7.4Aoo I 0.A739 8.0800 I 0.9074 (,.2900 I 0.79A7 (,.8900 I o. A382 7.4900 I 0.A745 A.0900 I 0.9079 (,.3000 I 0.7993 6.9000 I o. A3AA 7.5000 I 0.8751 8.1000 I 0.90A5
6.3100 I o.Aooo (,.9100 I 0.8395 7.5100 I 0.8756 8.1100 I 0.9090 6.3200 I 0.Ao07 6.9?00 I 0.8401 7.5200 I 0.8762 8.1200 I 0.909(, 6.3300 I 0.8014 6.9300 I 0.A407 7.5300 I 0.8768 8.1300 I 0.9101 (,.3400 I 0.A021 6.9400 I 0.A414 7.5400 I 0.8774 8.1400 I 0.910(, 6.3500 I 0.A02A 6.9500 I 0.A420 7.5500 I 0.8779 8.1500 I 0.9112 (,.3600 I 0.8035 (,.9600 I 0.842(, 7.5600 I 0.8785 8.1600 I 0.9117 (,.3700 I 0.A041 6.9700 I 0.A432 7.5700 I 0.8791 A.17oo I 0.9122 (,.3Aoo I 0.A04A (,.9Aoo I 0.A439 7.5800 I 0.A797 8.1Aoo I 0.91?A (,.3900 I 0.AoS5 (,.9900 I 0.A445 7.5900 I 0.AA02 A.1900 I 0.9133 (,.4000 I 0.Ao(,2 7.0000 I 0.A451 7.6000 I 0.880B A.2000 I 0.913B
274
Fortsetzung Tabelle 20
X LOGX X LOGX X LOGX
8.~100 I 0.9143 8.8100 I 0.9450 9.4100 I 0.9736 8.~200 I 0.9149 8.8~00 I 0.9455 9.4~00 I 0.9741 8.2300 I 0.9154 8.8100 I 0.9460 9.4300 I 0.9745 8.~400 I 0.9159 8.8400 I 0.9465 9.4400 I 0.9750 8.~500 I 0.911',5 8.8500 I 0.94li9 9.4500 I 0.9754 8.~600 I 0.9170 8.8600 I 0.9474 g.4600 I 0.9759 8.2700 I 0.9175 8.8700 I 0.9479 9.4700 I 0.9763 8.2800 I 0.9180 8.8800 I 0.9484 9.4800 I 0.971)8 8.2900 I 0.9181i R.8900 I 0.9489 9.4900 I 0.9773 R.looo I 0.9111 8.9000 I 0.9494 9.5000 I 0.9777
8.3100 I 0.,)19( 8.9100 I 0.94')') 9.5100 I 0.'l78~ 8. <200 I 0.,)201 R.9200 I 0.')504 ').5200 I 0.978( R.3300 I 0.9201i 8.9300 I 0.9509 9.5100 I 0.9791 8.3400 I 0.9212 8.9400 I 0.9513 9.5400 I 0.9795 8.1500 I o. 9~17 8.9500 I 0.951R 9.5500 I 0.9Roo 8.3lioo I 0.9222 8.9lioo I 0.95~3 9.5600 I 0.9805 8.1700 I 0.9227 R.97oo I 0.9528 9.5700 I 0.9809 R.3Roo I 0.9232 8.9800 I 0.9533 9.5800 I 0.9814 8. J900 I 0.9238 8.9900 I 0.9538 9.5900 I 0.981R fl.4000 I 0.9243 9.0000 I 0.9542 9.liooo I 0.982)
8.4100 I 0.9?48 9.0100 I 0.9547 9.liloo I 0.9827 8.4200 I 0.9251 9.0200 I 0.9552 9J,200 I 0.9832 R.4300 I 0.9258 9.0100 I 0.9557 9.6300 I 0.9836 8.4400 I 0.926) 9.0400 I 0.9562 9.li400 I 0.9841 8.4500 I 0.9269 9.0500 I 0.9566 9.6500 I 0.9845 8.4!ioo I 0.9274 9.0600 I 0.9571 9.fifioo I 0.9850 8.4700 I 0.9279 9.0700 I 0.957fi 9.fi700 I 0.9854 8.4Roo I 0.9284 9.0800 I 0.9581 9.fi800 I 0.9859 8.4900 I 0.9289 9.0900 I 0.958fi 9.fi900 I 0.98fi3 8.5000 I 0.9294 9.1000 I 0.9590 9.7000 I 0.98fiR
8.5100 I 0.9299 9.1100 I 0.9595 9.7100 I 0.9872 8.5200 I 0.9304 9.1200 I 0.9fioo 9.7200 I 0.9877 8.5300 I 0.9309 9.1300 I 0.9605 9.7300 I 0.9881 8.5400 I 0.9315 9.1400 I 0.9609 9.7400 I 0.98Rfi 8.5500 I 0.9320 9.1500 I 0.9fi14 9.7500 I 0.9890 8.Shoo I 0.9325 9.1600 I 0.9!i19 9.7fioo I 0.9894 8.5700 I 0.9330 9.1700 I 0.9624 9.7700 I 0.9899 fl.5floo I 0.9335 9.1Roo I 0.9fi28 9.7800 I 0.9903 8.5900 I 0.9340 9.1900 I 0.9li33 9.7900 I 0.9908 8.fiooo I 0.9345 9.2000 I 0.9fi3fl 9.8000 I 0. 9912
8.6100 I 0.9350 °.2100 I 0.9fi43 9.8100 I 0.9917 8.li200 I 0.9355 9.2200 I 0.9(;47 9.f1200 I 0.9921 8. !i300 I 0.9360 9.2300 I 0.9fi52 9.8300 I 0.992fi fl.fAoo I 0.93fi5 9.2400 I 0.9(,'>7 9.8400 I 0.9930 8.6500 I 0.9370 9.2500 I 0.9fi('1 9.8500 I 0.9934 8.6fioo I 0.9375 9.2fioo I 0.966(, 9.8fioo I 0.9939 8.fi700 I 0.9380 9.2700 I 0.9fi71 9.8700 I 0.9943 8.fi800 I 0.93fl5 9.2800 I 0.9fi75 9.8800 I 0.9948 8.6900 I 0.9390 9.2900 I 0.9fi80 9.8900 I 0.9952 8.7000 I 0.9395 9.3000 I 0.9685 9.9000 I 0.995(,
8.7100 I 0.9400 9.3100 I 0.9689 9.9100 I 0.9961 8.7200 I 0.9405 9.3200 I 0.9694 9.9200 I 0.9965 8.7300 I 0.9410 9.3300 I 0.9699 9.9300 I 0.9969 8.7400 I 0.9415 9.3400 I 0.9703 9.9400 I 0.9974 8.7500 I 0.9420 9.3500 I 0.9708 9.9500 I 0.9978 8.7600 I 0.9425 9.3600 I 0.9713 9.9600 I 0.9983 8.7700 I 0.9430 9.3700 I 0.9717 9.9700 I 0.9987 8.7800 I 0.9435 9.3800 I 0.9722 9.9800 I 0.9991 8.7900 I 0.9440 9.3900 I 0.9727 9.9900 I 0.9996 8.8000 I 0.9445 9.4000 I 0.9731 10.0000 I 1.0000
275
REGISTER
Abbildung 21 Abgang 52 -, durchschnittlicher 58 Ableitung 34 -, partielle 42 Abweichung, durchschnittliche 79 -, mittlere quadratische 79,81,82 Aggregatform 115 a-Punkt 147 asymptotisch normalverteilt 187 Axiome der Wahrscheinlichkeitsrechnung 131 Bayes, Formel von 141 f. Beobachtungswert 51,72 Bestand 52 Bestandsmasse 52 Bewegungsmasse 52 Bild.m.enge 21 Binomialkoeffizient 46 Binomialverteilung 151,167 f.,175,183 i-Test 232 ff. x2-Verteilung 171,175 Definitionsbereich 21 Determinationskoeffizient 93 Dichtefunktion 153 -, gemeinsame 161 Differenzenschatzung 245 f. Durchschnittsbestand 55 Elementarereignis 130 -, Menge der -se 130 Ereignis 130
paarweise unabhangige -se 136 -, unabhangige -se 136 -, Wahrscheinlichkeit eines -ses 131,145,147 Ereignisring 130
276
Erhebung 51 Erwartungswert 175 ff.,179 f.
euklidischer Raum 20 F-Verteilung 174 Faktorumkehrprobe 113,116 Fakultat 46 Folge 26 -, divergente 27 -, konvergente 27 Fortschreibungsformel 53 Funktion, Ableitung einer 34
diskrete 23 , kO:J.tinuierliche 23
Konvergenz einer 32 reelle 22 Sprungstelle einer 33 stetige 33 stuckweise stetige 33
Funktional 22 Gesetz der groBen Zahl 186 Gesamtverweildauer 56 Gewicht 78,114 Gleichverteilung 154 gleitende Durchschnitte 106 gleitende 12-l"lonatsdurchschnitte 107 n. Grenzwert einer Folge 27 - einer Funktion 32 Grenzwertsatz von Lindeberg-Levy 188 - von Ljapunoff 187 f.
-, zentraler 187 Grundgesamtheit 189 -, hypothetische 191 -, Verteilung einer 192 gruppierte Daten 66,69 Haufigkeit, absolute 59 -, gemeinsame 60 f.
277
Haufigkeit, kumulierte 65,69 -, relative 59 -, relative prozentuale 59 Haufigkeitsdiagramm 62 Haufigkeitskurve, kumulierte 69 Haufigkeitspolygon 66 Haufigkeitsverteilung 59 Histogramm 66 Hochrechnung 245 f. Identitatsprobe 113,116 Indexzahlen 114 ff. Integral, bestimmtes 39 -, mehrfaches 45 -, uneigentliches 41 Intervall 16 -, n-dimensionales 20 -, unendliches -16
Intervallschatzung 210 Klassenbreite 66 Klassengrenze 66 Klassenhaufigkeit 66
Klassenmitte 66 Kleinst-Quadrate-Schatzung 205 ff. Klumpen 244 Klumpenstichprobe 2~} f. Kombination 49 Komplement einer Menge 15 Komponente, glatte 101 -, irregulare 98 -, zyklische 98 Konfidenzintervall 210 -, symmetrisches 210 Konfidenzniveau 210 Kontingenztabellen 234 ff. Konzentrationskurve 70 Korrelationskoeffizient 84,177,203,220
278
Korrelationskoeffizient von Bravais-Pearson 87 ff. - von Fechner 86 f. Kovarianz 177 kritischer Wert 219 Lageregel 73 Lorenzkurve 71 Masse, statistische 52
geschlossene, statistische 55 -, offene, statistische 55 -, stationare, statistische 55 I1aBzahlen 72 Median 72 Menge 13
abziihlbare 14 , disjunkte -n 17
Durchschnitt vo~ -n 17 Element einer 13 endliche 14 hochstens abziihlbare 14
, Komplement einer 15 leere 13
, Produkt von -n 19 Teilmenge einer 14
, Umfang einer 14 , Vereinigung von -n 17 f.
Zerlegung von -n 18 Mengenring 18 Merkmal 51
quantitatives 62 -, quantifiziertes 62 -, qualitatives 62 Merkmalsauspragung 51 Merkmalstrager 51 MeBzahlen 112 ff. Methode der kleinsten Quadrate 43,93,103,205 f. Methode der Reihenhalften 102
279
Mittel, arithmetisches 73,75 ff. -, geometrisches 74 -, gewogenes arithmetisches 78 Mittelwert 72 Modus 73 Moment 176 n-tupel 19 Normalgleichungen 44 Normalverteilung 155,183
Additionstheorem der 171 -, standardisierte 155 -, zweidimensionale 162,220 Parameter einer Verteilung 197 Permutation 48 Poissonverteilung 152,175,183 Preisbereinigung 120 f. Proportionalitatsprobe 113,116 Punktschatzung 197 Randhaufigkeit 61 Randverteilung 158 Rangkorrelationskoeffizient von Spearman 91 Regression, einfache lineare 91 -, multiple lineare 96 Regressionsgerade 92,208 Regressionskoeffizient 93,96,208 Reihenglattung 106 Rundprobe 113,116 Saiso~bereinigung 95 ff. Saisonfigur 101 Saisonkomponente 98 Schatzfunktion 197,205
280
effiziente 198 erwartungstreue 197 wirksamere 198 asymptotisch erwartungstreue Folge von -en 200 asymptotisch normale Folge von -en 200
Schatzfunktion, konsistente Folge von -en 199 Schatzwert 197 Schichten 242 Schwarzsche Ungleichung 30 a-Ring 19,130 Signifikanzniveau 218 Signifikanztest 218 Spannwei te 79 Stabdiagramm 62 Stammfunktion 37 Standardabweichung 80 Stichprobe 189 ff.,195 -, geschichtete 242 ff. Stichproben ohne Zurlicklegen 241 ff. Stichprobenfunktion 196 Stichprobenraum 193,195 Stichprobenvariable 193,195 Stichprobenverteilung 196 Stichprobenwerte 193 Streudiagramm 85 Streuung 176 StreuungsmaB 79 -, relatives 80 Summenzeichen 29
t-Test 219 ff. t-Verteilung 173,175 Teilmenge 14 Test, statistischer 218 -, verteilungsfreier statistischer 237 Testfunktion 219 -, asymptotisch normalverteilte 223 ff. Te stwert 219 Trend 98 Treppenfunktion 33 Tschebyscheff, Ungleichung von 184 Umbasierung 106
281
Umschlagshaufigkeit 58 unendliche Reihe 30 Urnenmodell 128 Variable 22 -, Realisation einer -n 22 Varianz 176,179 ff. Varianzanalyse 229 ff. Variationskoeffizient 80 Verkettung 113,118 Verknupfung 119 Verteilung 149
Approximation von -en 174 f. diskrete 149 ff. kontinuierliche 153 ff. mehrdimensionale 156 ff.
Verteilungsfunktion 145 - einer zweidimensionalen Zufallsvariablen 157 -, gemeinsame 158 Vertrauensgrenzen 210 Vertrauenswahrscheinlichkeit 210 Verweildauer 52,56 Verweillinie 53 Vorzeichentest 237 ff. Wahrscheinlichkeit, bedingte 139 f. -, klassische 125 -, statistische 124 Wahrscheinlichkeitsfeld 131 Wahrscheinlichkeitsfunktion 149 -, gemeinsame 158 Wahrscheinlichkeitsfunktional 130 Zahlenfolge 27 Zahlenmenge 15 -, diskrete -n 16 Zahlentupel 20 Zeitreihe 97 Zeitreihenanalyse 98
282
Zeitreihendiagramm 97 Zeitreihenpolygon 98 Zeitumkehrprobe 113,116 Zerlegung 18 ZUfallsauswahl, uneingeschrankte 190 Zufallsergebnis 123 Zufallsstichprobe, einfache, vom Umfang Eins 192 -, einfache, vom Umfang n 194 f. -, einfache verbundene 200 Zufallsvariable 143 f.
Folge von -n 184 ff.,187 f. , Funktionen von normalverteilten -n 169 ff.
Funktionen von -n 165 ff. paarweise unabhangige -n 164
, standardisierte 177 unabhangige -n 163 ff.,180 unkorrelierte -n 177,180 zweidimensionale 156
Zufallsvorgang 123 Zufallswert 144,149 -, Menge der -e 144 Zufallszahlen 190 Zugang 52
Bucher fur Ihr Studium
Agnes Reichardt Obungsbuch zur Statistischen Methodenlehre
ca. 100 Aufgaben mit Losungen
Lehrbuch der Mathematik fUr Wirtschaftswissenschaften
Herausgegeben von Heinz Korth, Carl Otto, Walter Runge, Manfred Schoch
Das Such bietet dem Leser den gesamten mathematischen Lehrstoff, der zur Zeit fur Studenten an den Wirtschaftswissenschaftlichen Hochschulen und Fakultaten und fur Wirtschaftsingenieure grundlegend ist.
Gunter Menges Grundmodelle wirtschaftlicher Entscheidungen
Einfuhrung in moderne Entscheidungstheorien unter besonderer Serucksichtigung volks- und betriebswirtschaftlicher Anwendungen.
"Menges legt mit seinem Werk uber Entscheidungstheorien ein modernes Kompendium vor, das nicht nur fur Experten interessant ist. Trotz der Vielzahl mathematischer Formeln werden nur geringe mathematische Kenntnisse vorausgesetzt, da der Leser Schritt fUr Schritt in die Materie eingefuhrt wird. Sei der LekWre kann der Leser sein Verstandnis durch gut gewahlte Seispiele laufend kontrollieren. Fur die Hand des Volkswirtes durfte dieses Such sich als unentbehrlich erweisen, da es die wichtigsten Gebiete der Methodenlehre der modernen ·Statistik berucksichtigt." Handelsblatt
Siegmar Stoppler Mathematik fUr Wirtschaftswissenschaftler: Lineare Algebra und okonomische Anwendung
Zentrales Gebiet der heutigen Mathematik fUr Wirtschaftswissenschaftler ist die Lineare Algebra. Das Such bietet eine EinfUhrung in die allgemeinen mathematischen Grundlagen als auch in die Vektoren- und Matrizenrechnung einschlieBlich der Linearen Programmierung.
Westdeutscher Verlag
