05 Tablice podstawowych rozkładów


Overview

Rozkł_normalny_dystrybuanta
Rozkł T, chi-kwadrat, Poisson
Rozkł_liczby_znaków
Rozkład_serii_1
Rozkład_serii_2
Lambda_Kołmogorow
T w granicy w nieskończ


Sheet 1: Rozkł_normalny_dystrybuanta

Dystrybuanta rozkładu normalnego





































x 0 1 2 3 4 5 6 7 8 9 .












0,0 0,50000 0,50399 0,50798 0,51197 0,51595 0,51994 0,52392 0,52790 0,53188 0,53586
0,1 0,53983 0,54380 0,54776 0,55172 0,55567 0,55962 0,56356 0,56749 0,57142 0,57535
0,2 0,57926 0,58317 0,58706 0,59095 0,59483 0,59871 0,60257 0,60642 0,61026 0,61409
0,3 0,61791 0,62172 0,62552 0,62930 0,63307 0,63683 0,64058 0,64431 0,64803 0,65173
0,4 0,65542 0,65910 0,66276 0,66640 0,67003 0,67364 0,67724 0,68082 0,68439 0,68793
0,5 0,69146 0,69497 0,69847 0,70194 0,70540 0,70884 0,71226 0,71566 0,71904 0,72240
0,6 0,72575 0,72907 0,73237 0,73565 0,73891 0,74215 0,74537 0,74857 0,75175 0,75490
0,7 0,75804 0,76115 0,76424 0,76730 0,77035 0,77337 0,77637 0,77935 0,78230 0,78524
0,8 0,78814 0,79103 0,79389 0,79673 0,79955 0,80234 0,80511 0,80785 0,81057 0,81327
0,9 0,81594 0,81859 0,82121 0,82381 0,82639 0,82894 0,83147 0,83398 0,83646 0,83891












1,0 0,84134 0,84375 0,84614 0,84849 0,85083 0,85314 0,85543 0,85769 0,85993 0,86214
1,1 0,86433 0,86650 0,86864 0,87076 0,87286 0,87493 0,87698 0,87900 0,88100 0,88298
1,2 0,88493 0,88686 0,88877 0,89065 0,89251 0,89435 0,89617 0,89796 0,89973 0,90147
1,3 0,90320 0,90490 0,90658 0,90824 0,90988 0,91149 0,91309 0,91466 0,91621 0,91774
1,4 0,91924 0,92073 0,92220 0,92364 0,92507 0,92647 0,92785 0,92922 0,93056 0,93189
1,5 0,93319 0,93448 0,93574 0,93699 0,93822 0,93943 0,94062 0,94179 0,94295 0,94408
1,6 0,94520 0,94630 0,94738 0,94845 0,94950 0,95053 0,95154 0,95254 0,95352 0,95449
1,7 0,95543 0,95637 0,95728 0,95818 0,95907 0,95994 0,96080 0,96164 0,96246 0,96327
1,8 0,96407 0,96485 0,96562 0,96638 0,96712 0,96784 0,96856 0,96926 0,96995 0,97062
1,9 0,97128 0,97193 0,97257 0,97320 0,97381 0,97441 0,97500 0,97558 0,97615 0,97670












2,0 0,97725 0,97778 0,97831 0,97882 0,97932 0,97982 0,98030 0,98077 0,98124 0,98169
2,1 0,98214 0,98257 0,98300 0,98341 0,98382 0,98422 0,98461 0,98500 0,98537 0,98574
2,2 0,98610 0,98645 0,98679 0,98713 0,98745 0,98778 0,98809 0,98840 0,98870 0,98899
2,3 0,98928 0,98956 0,98983 0,99010 0,99036 0,99061 0,99086 0,99111 0,99134 0,99158
2,4 0,99180 0,99202 0,99224 0,99245 0,99266 0,99286 0,99305 0,99324 0,99343 0,99361
2,5 0,99379 0,99396 0,99413 0,99430 0,99446 0,99461 0,99477 0,99492 0,99506 0,99520
2,6 0,99534 0,99547 0,99560 0,99573 0,99585 0,99598 0,99609 0,99621 0,99632 0,99643
2,7 0,99653 0,99664 0,99674 0,99683 0,99693 0,99702 0,99711 0,99720 0,99728 0,99736
2,8 0,99744 0,99752 0,99760 0,99767 0,99774 0,99781 0,99788 0,99795 0,99801 0,99807
2,9 0,99813 0,99819 0,99825 0,99831 0,99836 0,99841 0,99846 0,99851 0,99856 0,99861












3,0 0,9986501 0,9986938 0,9987361 0,9987772 0,9988171 0,9988558 0,9988933 0,9989297 0,9989650 0,9989992
3,1 0,9990324 0,9990646 0,9990957 0,9991260 0,9991553 0,9991836 0,9992112 0,9992378 0,9992636 0,9992886
3,2 0,9993129 0,9993363 0,9993590 0,9993810 0,9994024 0,9994230 0,9994429 0,9994623 0,9994810 0,9994991
3,3 0,9995166 0,9995335 0,9995499 0,9995658 0,9995811 0,9995959 0,9996103 0,9996242 0,9996376 0,9996505
3,4 0,9996631 0,9996752 0,9996869 0,9996982 0,9997091 0,9997197 0,9997299 0,9997398 0,9997493 0,9997585
3,5 0,9997674 0,9997759 0,9997842 0,9997922 0,9997999 0,9998074 0,9998146 0,9998215 0,9998282 0,9998347
3,6 0,9998409 0,9998469 0,9998527 0,9998583 0,9998637 0,9998689 0,9998739 0,9998787 0,9998834 0,9998879
3,7 0,9998922 0,9998964 0,9999004 0,9999043 0,9999080 0,9999116 0,9999150 0,9999184 0,9999216 0,9999247
3,8 0,9999277 0,9999305 0,9999333 0,9999359 0,9999385 0,9999409 0,9999433 0,9999456 0,9999478 0,9999499
3,9 0,9999519 0,9999539 0,9999557 0,9999575 0,9999593 0,9999609 0,9999625 0,9999641 0,9999655 0,9999670












4,0 0,9999683 0,9999696 0,9999709 0,9999721 0,9999733 0,9999744 0,9999755 0,9999765 0,9999775 0,9999784
4,1 0,9999793 0,9999802 0,9999811 0,9999819 0,9999826 0,9999834 0,9999841 0,9999848 0,9999854 0,9999861
4,2 0,9999867 0,9999872 0,9999878 0,9999883 0,9999888 0,9999893 0,9999898 0,9999902 0,9999907 0,9999911
4,3 0,9999915 0,9999918 0,9999922 0,9999925 0,9999929 0,9999932 0,9999935 0,9999938 0,9999941 0,9999943
4,4 0,9999946 0,9999948 0,9999951 0,9999953 0,9999955 0,9999957 0,9999959 0,9999961 0,9999963 0,9999964
4,5 0,9999966 0,9999968 0,9999969 0,9999971 0,9999972 0,9999973 0,9999974 0,9999976 0,9999977 0,9999978
4,6 0,9999979 0,9999980 0,9999981 0,9999982 0,9999983 0,9999983 0,9999984 0,9999985 0,9999986 0,9999986
4,7 0,9999987 0,9999988 0,9999988 0,9999989 0,9999989 0,9999990 0,9999990 0,9999991 0,9999991 0,9999992
4,8 0,9999992 0,9999992 0,9999993 0,9999993 0,9999994 0,9999994 0,9999994 0,9999994 0,9999995 0,9999995
4,9 0,9999995 0,9999995 0,9999996 0,9999996 0,9999996 0,9999996 0,9999996 0,9999997 0,9999997 0,9999997

Sheet 2: Rozkł T, chi-kwadrat, Poisson

Skrócona tabelka rozkładu t Studenta













Dla danej ilości r stopni swobody i liczby a tabela podaje wartość ta taką, że
P(|T|>ta)=a, gdzie T jest zmienną losową o rozkładzie t Studenta o r stopniach swobody













a= 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,05 0,04 0,02 0,01
r=











1 0,325 0,510 0,727 1,000 1,376 1,963 3,078 6,314 12,706 15,895 31,821 63,657
2 0,289 0,445 0,617 0,816 1,061 1,386 1,886 2,920 4,303 4,849 6,965 9,925
3 0,277 0,424 0,584 0,765 0,978 1,250 1,638 2,353 3,182 3,482 4,541 5,841
4 0,271 0,414 0,569 0,741 0,941 1,190 1,533 2,132 2,776 2,999 3,747 4,604
5 0,267 0,408 0,559 0,727 0,920 1,156 1,476 2,015 2,571 2,757 3,365 4,032
6 0,265 0,404 0,553 0,718 0,906 1,134 1,440 1,943 2,447 2,612 3,143 3,707
7 0,263 0,402 0,549 0,711 0,896 1,119 1,415 1,895 2,365 2,517 2,998 3,499
8 0,262 0,399 0,546 0,706 0,889 1,108 1,397 1,860 2,306 2,449 2,896 3,355
9 0,261 0,398 0,543 0,703 0,883 1,100 1,383 1,833 2,262 2,398 2,821 3,250
10 0,260 0,397 0,542 0,700 0,879 1,093 1,372 1,812 2,228 2,359 2,764 3,169













16 0,258 0,392 0,535 0,690 0,865 1,071 1,337 1,746 2,120 2,235 2,583 2,921













25 0,256 0,390 0,531 0,684 0,856 1,058 1,316 1,708 2,060 2,167 2,485 2,787













Skrócona tabelka rozkładu chi kwadrat













Dla danej ilości r stopni swobody i liczby a tabela podaje wartość (ca)^2 taką, że
P(c2>ca2)=a, gdzie c2 jest zmienną o rozkładzie chi kwadrat o r stopniach swobody













a= 0,99 0,98 0,95 0,90 0,80 0,20 0,10 0,05 0,02 0,01 0,001
r=











1 0,000157 0,000628 0,00393 0,0158 0,0642 1,642 2,706 3,841 5,412 6,635 10,828
2 0,0201 0,0404 0,103 0,211 0,446 3,219 4,605 5,991 7,824 9,210 13,816
3 0,115 0,185 0,352 0,584 1,005 4,642 6,251 7,815 9,837 11,345 16,266
4 0,297 0,429 0,711 1,064 1,649 5,989 7,779 9,488 11,668 13,277 18,467
5 0,554 0,752 1,145 1,610 2,343 7,289 9,236 11,070 13,388 15,086 20,515
6 0,872 1,134 1,635 2,204 3,070 8,558 10,645 12,592 15,033 16,812 22,458
7 1,239 1,564 2,167 2,833 3,822 9,803 12,017 14,067 16,622 18,475 24,322
8 1,646 2,032 2,733 3,490 4,594 11,030 13,362 15,507 18,168 20,090 26,124
9 2,088 2,532 3,325 4,168 5,380 12,242 14,684 16,919 19,679 21,666 27,877
10 2,558 3,059 3,940 4,865 6,179 13,442 15,987 18,307 21,161 23,209 29,588













16 5,812 6,614 7,962 9,312 11,152 20,465 23,542 26,296 29,633 32,000 39,252













25 11,524 12,697 14,611 16,473 18,940 30,675 34,382 37,652 41,566 44,314 52,620


























Dla danej wartości l tapela podaje wartość exp(-l) [do obliczania prawdopodobieństwa w rozkładzie Poissona]














0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,5 2,0

0,90484 0,81873 0,74082 0,67032 0,60653 0,54881 0,49659 0,44933 0,40657 0,36788 0,22313 0,13534

2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 7,0 8,0 9,0 10,0

0,08208 0,04979 0,03020 0,01832 0,011109 0,006738 0,004087 0,002479 0,0009119 0,0003355 0,0001234 0,0000454

Sheet 3: Rozkł_liczby_znaków

Tablica. Rozkład liczby znaków








n a n a n a n a
0,01 0,05 0,10 0,25 0,01 0,05 0,10 0,25 0,01 0,05 0,10 0,25 0,01 0,05 0,10 0,25
1
24 5 6 7 8 47 14 16 17 19 69 23 25 27 29
2
25 5 7 7 9 48 14 16 17 19 70 23 26 27 29
3 0 26 6 7 8 9 49 15 17 18 19 71 24 26 28 30
4 0 27 6 7 8 10 50 15 17 18 20 72 24 27 28 30
5 0 0 28 6 8 9 10 51 15 18 19 20 73 25 27 28 31
6 0 0 1 29 7 8 9 10 52 16 18 19 21 74 25 28 29 31
7 0 0 1 30 7 9 10 11 53 16 18 20 21 75 25 28 29 32
8 0 0 1 1 31 7 9 10 11 54 17 19 20 22 76 26 28 30 32
9 0 1 1 2 32 8 9 10 12 55 17 19 20 22 77 26 29 30 32
18 0 1 1 2 33 8 10 11 12 56 17 20 21 23 78 27 29 31 33
11 0 1 2 3 34 9 10 11 13 57 18 20 21 23 79 27 30 31 33
12 1 2 2 3 35 9 11 12 13 58 18 21 22 24 80 28 30 32 34
13 1 2 3 3 36 9 11 12 14 59 19 21 22 24 81 28 31 32 34
14 1 2 3 4 37 10 12 13 14 60 19 21 23 25 82 28 31 33 35
15 2 3 3 4 38 10 12 13 14 61 20 22 23 25 83 29 32 33 35
16 2 3 3 5 39 11 12 13 15 62 20 22 24 25 84 29 32 33 36
17 2 4 4 5 40 11 13 14 15 63 20 23 24 26 85 30 32 34 36
18 3 4 5 6 41 31 13 14 16 64 2t 23 24 26 86 30 33 34 37
19 3 4 5 6 42 12 14 15 16 65 21 24 25 27 87 31 33 35 37
20 3 5 5 6 43 12 14 15 17 66 22 24 25 27 88 31 34 35 38
21 4 5 6 7 44 13 15 16 17 67 22 25 26 28 89 31 34 36 38
22 4 5 6 7 45 13 15 16 18 68 22 25 26 28 90 32 35 36 39
22 4 6 7 8 46 13 15 16 18











Dla n>90 przybliżoną wartością r jest największa liczba całkowita mniejsza niż (n-1)/2-k(n+I)^(1/2), gdzie






dla alpha=0,01; 0,05; 0,10; 0,25 - k jest równe odpowiednio1,2879; 0,9800; 0,8224; 0,5752.







Sheet 4: Rozkład_serii_1

Tablica. Rozklad serii















































































a=0,025 a=0,975
n1-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 <-n1
n2\|/





































n2\|/
2


















4

















2
3


















5 6
















3
4


















5 7 8















4
5

2 2














5 7 8 9














5
6
2 2 3 3













5 7 8 9 10













6
7
2 2 3 3 3












5 7 9 10 11 12












7
8
2 3 3 3 4 4





-




5 7 9 10 11 12 13











8
9
2 3 3 4 4 5 5










5 7 9 11 12 13 13 14










9
10
2 3 3 4 5 5 5 6









5 7 9 11 12 13 14 15 15









10
11
2 3 4 4 5 5 6 6 7








5 7 9 11 12 13 14 15 16 16








11
12 2 2 3 4 4 5 6 6 7 7 7







5 7 9 11 12 13 15 15 16 17 18







12
13 2 2 3 4 5 5 6 6 7 7 8 8






5 7 9 11 13 14 15 16 17 18 18 19






13
14 2 2 3 4 5 5 6 7 7 8 8 9 9





5 7 9 11 13 14 15 16 17 18 19 19 20





14
15 2 3 3 4 5 6 6 7 7 8 8 9 9 10




5 7 9 11 13 14 15 17 17 18 19 20 21 21




15
16 2 3 4 4 5 6 6 7 8 8 9 9 10 10 11



5 7 9 11 13 15 16 17 18 19 20 20 21 22 22



16
17 2 3 4 4 5 6 7 7 8 9 9 10 10 11 11 11


5 7 9 11 13 15 16 17 18 19 20 21 22 22 23 24


17
18 2 3 4 5 5 6 7 8 8 9 9 10 10 11 11 12 12

5 7 9 11 13 15 16 17 18 19 20 21 22 23 24 24 25

18
19 2 3 4 5 6 6 7 8 8 9 10 10 11 11 12 12 13 13
5 7 9 11 13 15 16 17 19 20 21 22 22 23 24 25 25 26
19
20 2 3 4 5 6 6' 7 8 9 9 10 10 12 12 13 13 13 13 14 5 7 9 11 13 15 16 17 19 20 21 22 23 24 24 25 26 26 27 20








































Tablica. Rozkład serii (cd.)















































































a=0,05 a=0,95
n1-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 <-n1
n2\|/





































n2\|/
2


















4

















2
3


















5 6
















3
4

2















5 6 7















4
5
2 2 3














5 7 8 8














5
6
2 3 3 3













5 7 8 9 10













6
7
2 3 3 4 4












5 7 8 9 10 11












7
8 2 2 3 3 4 4 5











5 7 9 10 11 12 12











8
9 2 2 3 4 4 5 5 6










5 7 9 10 11 12 13 13










9
10 2 3 3 4 5 5 6 6 6









5 7 9 10 11 12 13 14 15









10
11 2 3 3 4 5 5 6 6 7 7








5 7 9 11 12 13 14 14 15 16








11
12 2 3 4 4 5 6 6 7 7 8 8







5 7 9 11 12 13 14 15 16 16 17







12
13 2 3 4 4 5 6 6 7 8 8 9 9






5 7 9 11 12 13 14 15 16 17 17 18






13
14 2 3 4 5 5 6 7 7 8 8 9 9 10





5 7 9 11 12 13 15 16 16 17 18 19 19





14
15 2 3 4 5 6 6 7 8 8 9 9 10 10 11




5 7 9 11 13 14 15 16 17 18 18 19 20 20




15
16 2 3 4 5 6 6 7 8 8 9 10 10 11 11 11



5 7 9 11 13 14 15 16 17 18 19 20 20 21 22



16
17 2 3 4 5 6 7 7 8 9 9 10 10 11 11 12 12


5 7 9 11 13 14 15 16 17 18 19 20 21 21 22 23


17
18 2 3 4 5 6 7 8 8 9 10 10 11 11 12 12 13 13

5 7 9 11 13 14 15 17 18 19 20 20 21 22 23 23 24

18
19 2 3 4 5 č 7 8 8 9 10 10 11 12 12 13 13 14 14
5 7 9 11 13 14 15 17 18 19 20 21 22 22 23 24 24 25
19
20 2 3 4 5 6 7 8 9 9 10 11 11 12 12 13 13 14 14 15 5 7 9 11 13 14 16 17 18 19 20 21 22 23 24 24 25 26 26 20








































c.d na następnym arkuszu







































Sheet 5: Rozkład_serii_2

Tablica. Rozkład serii (cd.)



(Początek - na poprzednim arkuszu)

































n1=n2 a n1=n2 a n1=n2 a n1=n2 a

0,025 0.05 0,95 0.975
0,025 0.05 0,95 0.975
0,025 0.05 0,95 0.975
0,025 0.05 0,95 0.975
10 6 6 15 15 33 25 26 41 42 56 46 47 66 67 79 67 69 90 92
11 7 7 16 16 34 26 27 42 43 57 47 48 67 68 80 68 70 91 93
12 7 8 17 18 35 27 28 43 44 58 47 49 68 70 81 69 71 92 94
13 8 9 18 19 36 28 29 44 45 59 48 50 69 71 82 69 71 94 96
14 9 10 19 20 37 29 30 45 46 60 49 51 70 72 83 70 72 95 97
15 10 11 20 21 38 30 31 46 47 61 50 52 71 73 84 71 73 96 98
16 11 11 22 22 39 30 32 47 49 62 51 53 72 74 85 72 74 97 99
17 11 12 23 24 40 31 33 48 50 63 52 54 73 75 86 73 75 98 100
18 12 13 24 25 41 32 34 49 51 64 53 55 74 76 87 74 76 99 101
19 13 14 25 26 42 33 35 50 52 65 54 56 75 77 88 75 77 100 102
20 14 15 26 27 43 34 35 52 53 66 55 57 76 78 89 76 78 101 103
21 15 16 27 28 44 35 36 53 54 67 56 58 77 79 90 77 79 102 104
22 16 17 28 29 45 36 37 54 55 68 57 58 79 80 91 78 80 103 105
23 16 17 30 31 46 37 38 55 56 69 58 59 80 81 92 79 81 104 106
24 17 18 31 32 47 38 39 56 57 70 58 60 81 83 93 80 82 105 107
25 18 19 32 33 48 38 40 57 59 71 59 61 82 84 94 81 83 106 108
26 19 20 33 34 49 39 41 58 60 72 60 62 83 85 95 82 84 107 109
27 20 21 34 35 50 40 42 59 61 73 61 63 84 86 96 82 85 108 111
28 21 22 35 36 51 41 43 60 62 74 62 64 85 87 97 83 86 109 112
29 22 23 36 37 52 42 44 61 63 75 63 65 86 88 98 84 87 110 113
30 22 24 37 39 53 43 45 62 64 76 64 66 87 89 99 85 87 112 114
31 23 25 38 40 54 44 45 64 65 77 65 67 88 90 100 86 88 113 115
32 24 25 40 41 55 45 46 65 66 78 66 68 89 91
















































































































































































































































































































































































































































































c.d na następnym arkuszu



















Sheet 6: Lambda_Kołmogorow

Rozkład lambda Kołmogorowa (graniczny)




























x Q(x)
x Q(x)
x Q(x)
x Q(x)
x Q(x)
0,30 0,000009
0,80 0,455857
1,30 0,931908
1,80 0,996932
2,30 0,999949
0,31 0,000021
0,81 0,472041
1,31 0,935370
1,81 0,997146
2,31 0,999954
0,32 0,000046
0,82 0,488030
1,32 0,938682
1,82 0,997346
2,32 0,999958
0,33 0,000091
0,83 0,503808
1,33 0,941848
1,83 0,997533
2,33 0,999962
0,34 0,000171
0,84 0,519366
1,34 0,944872
1,84 0,997707
2,34 0,999965
0,35 0,000303
0,85 0,534682
1,35 0,947756
1,85 0,997870
2,35 0,999968
0,36 0,000511
0,86 0,549744
1,36 0,950512
(~0,95)

1,86 0,998023
2,36 0,999970
0,37 0,000826
0,87 0,564546
1,37 0,953142
1,87 0,998145
2,37 0,999973
0,38 0,001285
0,88 0,579070
1,38 0,955650
1,88 0,998297
2,38 0,999976
0,39 0,001929
0,89 0,593316
1,39 0,958040
1,89 0,998421
2,39 0,999978
0,40 0,002808
0,90 0,607270
1,40 0,960318
1,90 0,998536
2,40 0,999980
0,41 0,003972
0,91 0,620928
1,41 0,962486
1,91 0,998644
2,41 0,999982
0,42 0,005476
0,92 0,634216
1,42 0,964552
1,92 0,998744
2,42 0,999984
0,43 0,007377
0,93 0,647338
1,43 0,966516
1,93 0,998837
2,43 0,999986
0,44 0,009730
0,94 0,660062
1,44 0,968382
1,94 0,998924
2,44 0,999987
0,45 0,012590
0,95 0,672516
1,45 0,970158
1,95 0,999004
(~0,999)

2,45 0,999988
0,46 0,016005
0,96 0,684636
1,46 0,971846
1,96 0,999079
2,46 0,999989
0,47 0,020022
0,97 0,696444
1,47 0,973448
1,97 0,999149
2,47 0,999990
0,48 0,024682
0,98 0,707940
1,48 0,974970
1,98 0,999213
2,48 0,999991
0,49 0,030017
0,99 0,719126
1,49 0,976412
1,99 0,999273
2,49 0,999992
0,50 0,036055
1,00 0,730000
1,50 0,977782
2,00 0,999329
2,50 0,9999925
0,51 0,042814
1,01 0,740566
1,51 0,979080
(~0,98)

2,01 0,999380
2,55 0,9999956
0,52 0,050306
1,02 0,750826
1,52 0,980310
2,02 0,999428
2,60 0,9999974
0,53 0,058534
1,03 0,760780
1,53 0,981476
2,03 0,999474
2,65 0,9999984
0,54 0,067497
1,04 0,770434
1,54 0,982578
2,04 0,999516
2,70 0,9999990
0,55 0,077183
1,05 0,779794
1,55 0,983622
2,05 0,999552
2,75 0,9999994
0,56 0,087577
1,06 0,788860
1,56 0,984610
2,06 0,999588
2,80 0,9999997
0,57 0,098656
1,07 0,797636
(~0,8)

1,57 0,985544
2,07 0,999620
2,85 0,99999982
0,58 0,110395
1,08 0,806128
1,58 0,986426
2,08 0,999650
2,90 0,99999990
0,59 0,122760
1,09 0,814342
1,59 0,987260
2,09 0,999680
2,95 0,99999994
0,60 0,135718
1,10 0,822282
1,60 0,988048
2,10 0,999705
3,00 0,99999997
0,61 0,149229
1,11 0,829950
1,61 0,988791
2,11 0,999723


0,62 0,163225
1,12 0,837356
1,62 0,989492
2,12 0,999750


0,63 0,177753
1,13 0,844502
1,63 0,990154
(~0,99)

2,13 0,999770


0,64 0,192677
1,14 0,851394
1,64 0,990777
2,14 0,999790


0,65 0,207987
1,17 0,858038
1,65 0,991364
2,15 0,999806


0,66 0,223637
1,16 0,864442
1,66 0,991917
2,16 0,999822


0,67 0,239582
1,17 0,870612
1,67 0,992438
2,17 0,999838


0,68 0,255780
1,18 0,876548
1,68 0,992928
2,18 0,999852


0,69 0,272189
1,19 0,882258
1,69 0,993389
2,19 0,999864


0,70 0,288765
1,20 0,887750
1,70 0,993828
2,20 0,999874


0,71 0,305471
1,21 0,893030
1,71 0,994230
2,21 0,999886


0,72 0,322265
1,22 0,898104
(~0,9)

1,72 0,994612
2,22 0,999896


0,73 0,339113
1,23 0,902972
1,73 0,994972
2,23 0,999904


0,74 0,355981
1,24 0,907648
1,74 0,995309
2,24 0,999912


0,75 0,372833
1,25 0,912132
1,75 0,995625
2,25 0,999920


0,76 0,389640
1,26 0,916432
1,76 0,995922
2,26 0,999926


0,77 0,406372
1,27 0,920556
1,77 0,996200
2,27 0,999934


0,78 0,423002
1,28 0,924505
1,78 0,996460
2,28 0,999940


0,79 0,439505
1,29 0,928288
1,79 0,996704
2,29 0,999944



Sheet 7: T w granicy w nieskończ

Ten arkusz służy jedynie ilustracji pewnej własności rozkładu t Studenta


























Skrócona tabelka rozkładu t Studenta













Dla danej ilości r stopni swobody i liczby a tabela podaje wartość ta taką, że
P(|T|>ta)=a, gdzie T jest zmienną losową o rozkładzie t Studenta o r stopniach swobody













a= 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,05 0,04 0,02 0,01
r=











1 0,325 0,510 0,727 1,000 1,376 1,963 3,078 6,314 12,706 15,895 31,821 63,657
2 0,289 0,445 0,617 0,816 1,061 1,386 1,886 2,920 4,303 4,849 6,965 9,925
3 0,277 0,424 0,584 0,765 0,978 1,250 1,638 2,353 3,182 3,482 4,541 5,841
4 0,271 0,414 0,569 0,741 0,941 1,190 1,533 2,132 2,776 2,999 3,747 4,604
5 0,267 0,408 0,559 0,727 0,920 1,156 1,476 2,015 2,571 2,757 3,365 4,032
6 0,265 0,404 0,553 0,718 0,906 1,134 1,440 1,943 2,447 2,612 3,143 3,707
7 0,263 0,402 0,549 0,711 0,896 1,119 1,415 1,895 2,365 2,517 2,998 3,499
8 0,262 0,399 0,546 0,706 0,889 1,108 1,397 1,860 2,306 2,449 2,896 3,355
9 0,261 0,398 0,543 0,703 0,883 1,100 1,383 1,833 2,262 2,398 2,821 3,250
10 0,260 0,397 0,542 0,700 0,879 1,093 1,372 1,812 2,228 2,359 2,764 3,169













16 0,258 0,392 0,535 0,690 0,865 1,071 1,337 1,746 2,120 2,235 2,583 2,921













25 0,256 0,390 0,531 0,684 0,856 1,058 1,316 1,708 2,060 2,167 2,485 2,787













30 0,256 0,389 0,530 0,683 0,854 1,055 1,310 1,697 2,042 2,147 2,457 2,750
35 0,255 0,388 0,529 0,682 0,852 1,052 1,306 1,690 2,030 2,133 2,438 2,724
40 0,255 0,388 0,529 0,681 0,851 1,050 1,303 1,684 2,021 2,123 2,423 2,704
50 0,255 0,388 0,528 0,679 0,849 1,047 1,299 1,676 2,009 2,109 2,403 2,678
60 0,254 0,387 0,527 0,679 0,848 1,045 1,296 1,671 2,000 2,099 2,390 2,660
70 0,254 0,387 0,527 0,678 0,847 1,044 1,294 1,667 1,994 2,093 2,381 2,648
80 0,254 0,387 0,526 0,678 0,846 1,043 1,292 1,664 1,990 2,088 2,374 2,639
100 0,254 0,386 0,526 0,677 0,845 1,042 1,290 1,660 1,984 2,081 2,364 2,626
120 0,254 0,386 0,526 0,677 0,845 1,041 1,289 1,658 1,980 2,076 2,358 2,617
150 0,254 0,386 0,526 0,676 0,844 1,040 1,287 1,655 1,976 2,072 2,351 2,609
200 0,254 0,386 0,525 0,676 0,843 1,039 1,286 1,653 1,972 2,067 2,345 2,601
250 0,254 0,386 0,525 0,675 0,843 1,039 1,285 1,651 1,969 2,065 2,341 2,596
500 0,253 0,386 0,525 0,675 0,842 1,038 1,283 1,648 1,965 2,059 2,334 2,586
1000 0,253 0,385 0,525 0,675 0,842 1,037 1,282 1,646 1,962 2,056 2,330 2,581
2000 0,253 0,385 0,524 0,675 0,842 1,037 1,282 1,646 1,961 2,055 2,328 2,578
10000 0,253 0,385 0,524 0,675 0,842 1,036 1,282 1,645 1,960 2,054 2,327 2,576

0,253 0,385 0,524 0,675 0,842 1,036 1,282 1,645 1,960 2,054 2,327 2,576


























Powyższe ilustruje, jak rozkład t Studenta dąży do rozkładu normalnego




















































Skrócona tabelka rozkładu chi kwadrat













Dla danej ilości r stopni swobody i liczby a tabela podaje wartość (ca)^2 taką, że
P(c2>ca2)=a, gdzie c2 jest zmienną o rozkładzie chi kwadrat o r stopniach swobody













a= 0,99 0,98 0,95 0,90 0,80 0,20 0,10 0,05 0,02 0,01 0,001
r=











1 0,000157 0,000628 0,00393 0,0158 0,0642 1,642 2,706 3,841 5,412 6,635 10,828
2 0,0201 0,0404 0,103 0,211 0,446 3,219 4,605 5,991 7,824 9,210 13,816
3 0,115 0,185 0,352 0,584 1,005 4,642 6,251 7,815 9,837 11,345 16,266
4 0,297 0,429 0,711 1,064 1,649 5,989 7,779 9,488 11,668 13,277 18,467
5 0,554 0,752 1,145 1,610 2,343 7,289 9,236 11,070 13,388 15,086 20,515
6 0,872 1,134 1,635 2,204 3,070 8,558 10,645 12,592 15,033 16,812 22,458
7 1,239 1,564 2,167 2,833 3,822 9,803 12,017 14,067 16,622 18,475 24,322
8 1,646 2,032 2,733 3,490 4,594 11,030 13,362 15,507 18,168 20,090 26,124
9 2,088 2,532 3,325 4,168 5,380 12,242 14,684 16,919 19,679 21,666 27,877
10 2,558 3,059 3,940 4,865 6,179 13,442 15,987 18,307 21,161 23,209 29,588
11 3,053 3,609 4,575 5,578 6,989 14,631 17,275 19,675 22,618 24,725 31,264
12 3,571 4,178 5,226 6,304 7,807 15,812 18,549 21,026 24,054 26,217 32,909
13 4,107 4,765 5,892 7,042 8,634 16,985 19,812 22,362 25,472 27,688 34,528
14 4,660 5,368 6,571 7,790 9,467 18,151 21,064 23,685 26,873 29,141 36,123
15 5,229 5,985 7,261 8,547 10,307 19,311 22,307 24,996 28,259 30,578 37,697
16 5,812 6,614 7,962 9,312 11,152 20,465 23,542 26,296 29,633 32,000 39,252
17 6,408 7,255 8,672 10,085 12,002 21,615 24,769 27,587 30,995 33,409 40,790
18 7,015 7,906 9,390 10,865 12,857 22,760 25,989 28,869 32,346 34,805 42,312
19 7,633 8,567 10,117 11,651 13,716 23,900 27,204 30,144 33,687 36,191 43,820
20 8,260 9,237 10,851 12,443 14,578 25,038 28,412 31,410 35,020 37,566 45,315
21 8,897 9,915 11,591 13,240 15,445 26,171 29,615 32,671 36,343 38,932 46,797
22 9,542 10,600 12,338 14,041 16,314 27,301 30,813 33,924 37,659 40,289 48,268
23 10,196 11,293 13,091 14,848 17,187 28,429 32,007 35,172 38,968 41,638 49,728
24 10,856 11,992 13,848 15,659 18,062 29,553 33,196 36,415 40,270 42,980 51,179
25 11,524 12,697 14,611 16,473 18,940 30,675 34,382 37,652 41,566 44,314 52,620
26 12,198 13,409 15,379 17,292 19,820 31,795 35,563 38,885 42,856 45,642 54,052
27 12,879 14,125 16,151 18,114 20,703 32,912 36,741 40,113 44,140 46,963 55,476
28 13,565 14,847 16,928 18,939 21,588 34,027 37,916 41,337 45,419 48,278 56,892
29 14,256 15,574 17,708 19,768 22,475 35,139 39,087 42,557 46,693 49,588 58,301
30 14,953 16,306 18,493 20,599 23,364 36,250 40,256 43,773 47,962 50,892 59,703
31 15,655 17,042 19,281 21,434 24,255 37,359 41,422 44,985 49,226 52,191 61,098
32 16,362 17,783 20,072 22,271 25,148 38,466 42,585 46,194 50,487 53,486 62,487
33 17,074 18,527 20,867 23,110 26,042 39,572 43,745 47,400 51,743 54,776 63,870
34 17,789 19,275 21,664 23,952 26,938 40,676 44,903 48,602 52,995 56,061 65,247
35 18,509 20,027 22,465 24,797 27,836 41,778 46,059 49,802 54,244 57,342 66,619
36 19,233 20,783 23,269 25,643 28,735 42,879 47,212 50,998 55,489 58,619 67,985
37 19,960 21,542 24,075 26,492 29,635 43,978 48,363 52,192 56,730 59,893 69,346
38 20,691 22,304 24,884 27,343 30,537 45,076 49,513 53,384 57,969 61,162 70,703
39 21,426 23,069 25,695 28,196 31,441 46,173 50,660 54,572 59,204 62,428 72,055
40 22,164 23,838 26,509 29,051 32,345 47,269 51,805 55,758 60,436 63,691 73,402
41 22,906 24,609 27,326 29,907 33,251 48,363 52,949 56,942 61,665 64,950 74,745
42 23,650 25,383 28,144 30,765 34,157 49,456 54,090 58,124 62,892 66,206 76,084
43 24,398 26,159 28,965 31,625 35,065 50,548 55,230 59,304 64,116 67,459 77,419
44 25,148 26,939 29,787 32,487 35,974 51,639 56,369 60,481 65,337 68,710 78,750
45 25,901 27,720 30,612 33,350 36,884 52,729 57,505 61,656 66,555 69,957 80,077
46 26,657 28,505 31,439 34,215 37,795 53,818 58,641 62,830 67,771 71,201 81,400
47 27,416 29,291 32,268 35,081 38,708 54,906 59,774 64,001 68,985 72,443 82,720
48 28,177 30,080 33,098 35,949 39,621 55,993 60,907 65,171 70,197 73,683 84,037
49 28,941 30,871 33,930 36,818 40,534 57,079 62,038 66,339 71,406 74,919 85,351
50 29,707 31,664 34,764 37,689 41,449 58,164 63,167 67,505 72,613 76,154 86,661
51 30,475 32,459 35,600 38,560 42,365 59,248 64,295 68,669 73,818 77,386 87,968
52 31,246 33,256 36,437 39,433 43,281 60,332 65,422 69,832 75,021 78,616 89,272
53 32,018 34,055 37,276 40,308 44,199 61,414 66,548 70,993 76,223 79,843 90,573
54 32,793 34,856 38,116 41,183 45,117 62,496 67,673 72,153 77,422 81,069 91,872
55 33,570 35,659 38,958 42,060 46,036 63,577 68,796 73,311 78,619 82,292 93,168
56 34,350 36,464 39,801 42,937 46,955 64,658 69,919 74,468 79,815 83,513 94,461
57 35,131 37,270 40,646 43,816 47,876 65,737 71,040 75,624 81,009 84,733 95,751
58 35,913 38,078 41,492 44,696 48,797 66,816 72,160 76,778 82,201 85,950 97,039
59 36,698 38,888 42,339 45,577 49,718 67,894 73,279 77,931 83,391 87,166 98,324
60 37,485 39,699 43,188 46,459 50,641 68,972 74,397 79,082 84,580 88,379 99,607
61 38,273 40,512 44,038 47,342 51,564 70,049 75,514 80,232 85,767 89,591 100,888
62 39,063 41,327 44,889 48,226 52,487 71,125 76,630 81,381 86,953 90,802 102,166
63 39,855 42,143 45,741 49,111 53,412 72,201 77,745 82,529 88,137 92,010 103,442
64 40,649 42,960 46,595 49,996 54,336 73,276 78,860 83,675 89,320 93,217 104,716
65 41,444 43,779 47,450 50,883 55,262 74,351 79,973 84,821 90,501 94,422 105,988
66 42,240 44,599 48,305 51,770 56,188 75,424 81,085 85,965 91,681 95,626 107,258
67 43,038 45,421 49,162 52,659 57,115 76,498 82,197 87,108 92,860 96,828 108,526
68 43,838 46,244 50,020 53,548 58,042 77,571 83,308 88,250 94,037 98,028 109,791
69 44,639 47,068 50,879 54,438 58,970 78,643 84,418 89,391 95,213 99,228 111,055
70 45,442 47,893 51,739 55,329 59,898 79,715 85,527 90,531 96,388 100,425 112,317
71 46,246 48,720 52,600 56,221 60,827 80,786 86,635 91,670 97,561 101,621 113,577
72 47,051 49,548 53,462 57,113 61,756 81,857 87,743 92,808 98,733 102,816 114,835
73 47,858 50,377 54,325 58,006 62,686 82,927 88,850 93,945 99,904 104,010 116,092
74 48,666 51,208 55,189 58,900 63,616 83,997 89,956 95,081 101,074 105,202 117,346
75 49,475 52,039 56,054 59,795 64,547 85,066 91,061 96,217 102,243 106,393 118,599
76 50,286 52,872 56,920 60,690 65,478 86,135 92,166 97,351 103,410 107,583 119,850
77 51,097 53,705 57,786 61,586 66,409 87,203 93,270 98,484 104,576 108,771 121,100
78 51,910 54,540 58,654 62,483 67,341 88,271 94,374 99,617 105,742 109,958 122,348
79 52,725 55,376 59,522 63,380 68,274 89,338 95,476 100,749 106,906 111,144 123,594
80 53,540 56,213 60,391 64,278 69,207 90,405 96,578 101,879 108,069 112,329 124,839
81 54,357 57,051 61,261 65,176 70,140 91,472 97,680 103,010 109,232 113,512 126,083
82 55,174 57,890 62,132 66,076 71,074 92,538 98,780 104,139 110,393 114,695 127,324
83 55,993 58,729 63,004 66,976 72,008 93,604 99,880 105,267 111,553 115,876 128,565
84 56,813 59,570 63,876 67,876 72,943 94,669 100,980 106,395 112,712 117,057 129,804
85 57,634 60,412 64,749 68,777 73,878 95,734 102,079 107,522 113,871 118,236 131,041
86 58,456 61,255 65,623 69,679 74,813 96,799 103,177 108,648 115,028 119,414 132,277
87 59,279 62,098 66,498 70,581 75,749 97,863 104,275 109,773 116,184 120,591 133,512
88 60,103 62,943 67,373 71,484 76,685 98,927 105,372 110,898 117,340 121,767 134,745
89 60,928 63,788 68,249 72,387 77,622 99,991 106,469 112,022 118,495 122,942 135,978
90 61,754 64,635 69,126 73,291 78,558 101,054 107,565 113,145 119,648 124,116 137,208
91 62,581 65,482 70,003 74,196 79,496 102,117 108,661 114,268 120,801 125,289 138,438
92 63,409 66,330 70,882 75,100 80,433 103,179 109,756 115,390 121,954 126,462 139,666
93 64,238 67,179 71,760 76,006 81,371 104,241 110,850 116,511 123,105 127,633 140,893
94 65,068 68,028 72,640 76,912 82,309 105,303 111,944 117,632 124,255 128,803 142,119
95 65,898 68,879 73,520 77,818 83,248 106,364 113,038 118,752 125,405 129,973 143,344
96 66,730 69,730 74,401 78,725 84,187 107,425 114,131 119,871 126,554 131,141 144,567
97 67,562 70,582 75,282 79,633 85,126 108,486 115,223 120,990 127,702 132,309 145,789
98 68,396 71,434 76,164 80,541 86,065 109,547 116,315 122,108 128,849 133,476 147,010
99 69,230 72,288 77,046 81,449 87,005 110,607 117,407 123,225 129,996 134,642 148,230
100 70,065 73,142 77,929 82,358 87,945 111,667 118,498 124,342 131,142 135,807 149,449
101 70,901 73,997 78,813 83,267 88,886 112,726 119,589 125,458 132,287 136,971 150,667
102 71,737 74,853 79,697 84,177 89,826 113,786 120,679 126,574 133,431 138,134 151,884
103 72,575 75,709 80,582 85,088 90,767 114,845 121,769 127,689 134,575 139,297 153,099
104 73,413 76,566 81,468 85,998 91,709 115,903 122,858 128,804 135,718 140,459 154,314
105 74,252 77,424 82,354 86,909 92,650 116,962 123,947 129,918 136,860 141,620 155,528
106 75,092 78,282 83,240 87,821 93,592 118,020 125,035 131,031 138,002 142,780 156,740
107 75,932 79,142 84,127 88,733 94,534 119,078 126,123 132,144 139,143 143,940 157,952
108 76,774 80,001 85,015 89,645 95,477 120,135 127,211 133,257 140,283 145,099 159,162
109 77,616 80,862 85,903 90,558 96,419 121,192 128,298 134,369 141,423 146,257 160,372
110 78,458 81,723 86,792 91,471 97,362 122,250 129,385 135,480 142,562 147,414 161,581
111 79,302 82,584 87,681 92,385 98,306 123,306 130,472 136,591 143,700 148,571 162,788
112 80,146 83,447 88,570 93,299 99,249 124,363 131,558 137,701 144,838 149,727 163,995
113 80,991 84,310 89,461 94,213 100,193 125,419 132,643 138,811 145,975 150,882 165,201
114 81,836 85,173 90,351 95,128 101,137 126,475 133,729 139,921 147,111 152,037 166,406
115 82,682 86,037 91,242 96,043 102,081 127,531 134,813 141,030 148,247 153,191 167,610
116 83,529 86,902 92,134 96,958 103,025 128,587 135,898 142,138 149,383 154,344 168,813
117 84,377 87,767 93,026 97,874 103,970 129,642 136,982 143,246 150,517 155,496 170,016
118 85,225 88,633 93,918 98,790 104,915 130,697 138,066 144,354 151,652 156,648 171,217
119 86,074 89,500 94,811 99,707 105,860 131,752 139,149 145,461 152,785 157,800 172,418
120 86,923 90,367 95,705 100,624 106,806 132,806 140,233 146,567 153,918 158,950 173,617
121 87,773 91,234 96,598 101,541 107,751 133,861 141,315 147,674 155,051 160,100 174,816
122 88,624 92,102 97,493 102,458 108,697 134,915 142,398 148,779 156,183 161,250 176,014
123 89,475 92,971 98,387 103,376 109,643 135,969 143,480 149,885 157,314 162,398 177,212
124 90,327 93,840 99,283 104,295 110,589 137,022 144,562 150,989 158,445 163,546 178,408
125 91,180 94,710 100,178 105,213 111,536 138,076 145,643 152,094 159,575 164,694 179,604
126 92,033 95,580 101,074 106,132 112,483 139,129 146,724 153,198 160,705 165,841 180,799
127 92,887 96,451 101,971 107,051 113,430 140,182 147,805 154,302 161,834 166,987 181,993
128 93,741 97,322 102,867 107,971 114,377 141,235 148,885 155,405 162,963 168,133 183,186
129 94,596 98,194 103,765 108,891 115,324 142,288 149,965 156,508 164,091 169,278 184,379
130 95,451 99,066 104,662 109,811 116,272 143,340 151,045 157,610 165,219 170,423 185,571
131 96,307 99,939 105,560 110,732 117,219 144,392 152,125 158,712 166,346 171,567 186,762
132 97,163 100,812 106,459 111,652 118,167 145,444 153,204 159,814 167,473 172,711 187,953
133 98,020 101,686 107,357 112,573 119,116 146,496 154,283 160,915 168,600 173,854 189,142
134 98,878 102,560 108,257 113,495 120,064 147,548 155,361 162,016 169,725 174,996 190,331
135 99,736 103,435 109,156 114,417 121,012 148,599 156,440 163,116 170,851 176,138 191,520
136 100,595 104,310 110,056 115,338 121,961 149,651 157,518 164,216 171,976 177,280 192,707
137 101,454 105,185 110,956 116,261 122,910 150,702 158,595 165,316 173,100 178,421 193,894
138 102,314 106,061 111,857 117,183 123,859 151,753 159,673 166,415 174,224 179,561 195,080
139 103,174 106,938 112,758 118,106 124,809 152,803 160,750 167,514 175,348 180,701 196,266
140 104,034 107,815 113,659 119,029 125,758 153,854 161,827 168,613 176,471 181,840 197,451
141 104,896 108,692 114,561 119,953 126,708 154,904 162,904 169,711 177,594 182,979 198,635
142 105,757 109,570 115,463 120,876 127,658 155,954 163,980 170,809 178,716 184,118 199,819
143 106,619 110,448 116,366 121,800 128,608 157,004 165,056 171,907 179,838 185,256 201,002
144 107,482 111,327 117,268 122,724 129,558 158,054 166,132 173,004 180,959 186,393 202,184
145 108,345 112,206 118,171 123,649 130,508 159,104 167,207 174,101 182,080 187,530 203,366
146 109,209 113,086 119,075 124,574 131,459 160,153 168,283 175,198 183,200 188,666 204,547
147 110,073 113,965 119,979 125,499 132,409 161,202 169,358 176,294 184,321 189,802 205,727
148 110,937 114,846 120,883 126,424 133,360 162,251 170,432 177,390 185,440 190,938 206,907
149 111,802 115,726 121,787 127,349 134,311 163,300 171,507 178,485 186,560 192,073 208,086
150 112,668 116,608 122,692 128,275 135,263 164,349 172,581 179,581 187,678 193,208 209,265
151 113,533 117,489 123,597 129,201 136,214 165,398 173,655 180,676 188,797 194,342 210,443
152 114,400 118,371 124,502 130,127 137,165 166,446 174,729 181,770 189,915 195,476 211,620
153 115,266 119,253 125,408 131,054 138,117 167,495 175,803 182,865 191,033 196,609 212,797
154 116,134 120,136 126,314 131,980 139,069 168,543 176,876 183,959 192,150 197,742 213,973
155 117,001 121,019 127,220 132,907 140,021 169,591 177,949 185,052 193,267 198,874 215,149
156 117,869 121,903 128,127 133,835 140,973 170,639 179,022 186,146 194,384 200,006 216,324
157 118,738 122,786 129,034 134,762 141,926 171,686 180,094 187,239 195,500 201,138 217,499
158 119,607 123,671 129,941 135,690 142,878 172,734 181,167 188,332 196,616 202,269 218,673
159 120,476 124,555 130,848 136,618 143,831 173,781 182,239 189,424 197,731 203,400 219,846
160 121,346 125,440 131,756 137,546 144,783 174,828 183,311 190,516 198,846 204,530 221,019
161 122,216 126,325 132,664 138,474 145,736 175,875 184,382 191,608 199,961 205,660 222,191
162 123,086 127,211 133,572 139,403 146,689 176,922 185,454 192,700 201,076 206,790 223,363
163 123,957 128,097 134,481 140,331 147,643 177,969 186,525 193,791 202,190 207,919 224,535
164 124,828 128,983 135,390 141,260 148,596 179,016 187,596 194,883 203,303 209,047 225,705
165 125,700 129,870 136,299 142,190 149,549 180,062 188,667 195,973 204,417 210,176 226,876
166 126,572 130,757 137,209 143,119 150,503 181,109 189,737 197,064 205,530 211,304 228,045
167 127,445 131,644 138,118 144,049 151,457 182,155 190,808 198,154 206,642 212,431 229,215
168 128,318 132,532 139,028 144,979 152,411 183,201 191,878 199,244 207,755 213,558 230,383
169 129,191 133,420 139,939 145,909 153,365 184,247 192,948 200,334 208,867 214,685 231,552
170 130,064 134,308 140,849 146,839 154,319 185,293 194,017 201,423 209,978 215,812 232,719
171 130,938 135,197 141,760 147,769 155,273 186,338 195,087 202,513 211,090 216,938 233,887
172 131,813 136,086 142,671 148,700 156,228 187,384 196,156 203,602 212,201 218,063 235,053
173 132,687 136,975 143,582 149,631 157,182 188,429 197,225 204,690 213,311 219,189 236,220
174 133,563 137,865 144,494 150,562 158,137 189,475 198,294 205,779 214,422 220,314 237,385
175 134,438 138,755 145,406 151,493 159,092 190,520 199,363 206,867 215,532 221,438 238,551
176 135,314 139,645 146,318 152,425 160,047 191,565 200,432 207,955 216,641 222,563 239,716
177 136,190 140,536 147,230 153,356 161,002 192,610 201,500 209,042 217,751 223,687 240,880
178 137,066 141,427 148,143 154,288 161,957 193,654 202,568 210,130 218,860 224,810 242,044
179 137,943 142,318 149,056 155,220 162,913 194,699 203,636 211,217 219,969 225,933 243,207
180 138,820 143,210 149,969 156,153 163,868 195,743 204,704 212,304 221,077 227,056 244,370
181 139,698 144,101 150,882 157,085 164,824 196,788 205,771 213,391 222,185 228,179 245,533
182 140,576 144,994 151,796 158,018 165,780 197,832 206,839 214,477 223,293 229,301 246,695
183 141,454 145,886 152,709 158,951 166,735 198,876 207,906 215,563 224,401 230,423 247,857
184 142,332 146,779 153,623 159,883 167,691 199,920 208,973 216,649 225,508 231,544 249,018
185 143,211 147,672 154,538 160,817 168,647 200,964 210,040 217,735 226,615 232,665 250,179
186 144,090 148,565 155,452 161,750 169,604 202,008 211,106 218,820 227,722 233,786 251,339
187 144,970 149,459 156,367 162,684 170,560 203,052 212,173 219,906 228,828 234,907 252,499
188 145,850 150,352 157,282 163,617 171,517 204,095 213,239 220,991 229,935 236,027 253,659
189 146,730 151,247 158,197 164,551 172,473 205,139 214,305 222,076 231,040 237,147 254,818
190 147,610 152,141 159,113 165,485 173,430 206,182 215,371 223,160 232,146 238,266 255,976
191 148,491 153,036 160,028 166,419 174,387 207,225 216,437 224,245 233,251 239,386 257,135
192 149,372 153,931 160,944 167,354 175,343 208,268 217,502 225,329 234,356 240,505 258,292
193 150,254 154,826 161,860 168,288 176,301 209,311 218,568 226,413 235,461 241,623 259,450
194 151,135 155,722 162,776 169,223 177,258 210,354 219,633 227,496 236,566 242,742 260,607
195 152,017 156,617 163,693 170,158 178,215 211,397 220,698 228,580 237,670 243,860 261,763
196 152,900 157,513 164,610 171,093 179,172 212,439 221,763 229,663 238,774 244,977 262,920
197 153,782 158,410 165,527 172,029 180,130 213,482 222,828 230,746 239,877 246,095 264,075
198 154,665 159,306 166,444 172,964 181,087 214,524 223,892 231,829 240,981 247,212 265,231
199 155,548 160,203 167,361 173,900 182,045 215,567 224,957 232,912 242,084 248,329 266,386
200 156,432 161,100 168,279 174,835 183,003 216,609 226,021 233,994 243,187 249,445 267,541
201 157,316 161,998 169,196 175,771 183,961 217,651 227,085 235,077 244,290 250,561 268,695
202 158,200 162,895 170,114 176,707 184,919 218,693 228,149 236,159 245,392 251,677 269,849
203 159,084 163,793 171,032 177,643 185,877 219,735 229,213 237,240 246,494 252,793 271,002
204 159,969 164,691 171,951 178,580 186,835 220,777 230,276 238,322 247,596 253,908 272,155
205 160,854 165,590 172,869 179,516 187,793 221,818 231,340 239,403 248,698 255,023 273,308
206 161,739 166,488 173,788 180,453 188,752 222,860 232,403 240,485 249,799 256,138 274,460
207 162,624 167,387 174,707 181,390 189,710 223,901 233,466 241,566 250,900 257,253 275,612
208 163,510 168,286 175,626 182,327 190,669 224,943 234,529 242,647 252,001 258,367 276,764
209 164,396 169,186 176,546 183,264 191,628 225,984 235,592 243,727 253,102 259,481 277,915
210 165,283 170,085 177,465 184,201 192,586 227,025 236,655 244,808 254,202 260,595 279,066
211 166,169 170,985 178,385 185,139 193,545 228,066 237,717 245,888 255,302 261,708 280,217
212 167,056 171,885 179,305 186,076 194,504 229,107 238,780 246,968 256,402 262,821 281,367
213 167,943 172,785 180,225 187,014 195,463 230,148 239,842 248,048 257,502 263,934 282,517
214 168,831 173,686 181,145 187,952 196,423 231,189 240,904 249,128 258,601 265,047 283,666
215 169,718 174,587 182,066 188,890 197,382 232,230 241,966 250,207 259,701 266,159 284,815
216 170,606 175,488 182,987 189,828 198,341 233,270 243,028 251,286 260,800 267,271 285,964
217 171,494 176,389 183,907 190,767 199,301 234,311 244,090 252,365 261,898 268,383 287,112
218 172,383 177,291 184,828 191,705 200,260 235,351 245,151 253,444 262,997 269,495 288,261
219 173,271 178,192 185,750 192,644 201,220 236,391 246,213 254,523 264,095 270,606 289,408
220 174,160 179,094 186,671 193,582 202,180 237,432 247,274 255,602 265,193 271,717 290,556
221 175,050 179,996 187,593 194,521 203,140 238,472 248,335 256,680 266,291 272,828 291,703
222 175,939 180,899 188,514 195,460 204,100 239,512 249,396 257,758 267,389 273,939 292,850
223 176,829 181,801 189,436 196,400 205,060 240,552 250,457 258,837 268,486 275,049 293,996
224 177,719 182,704 190,359 197,339 206,020 241,592 251,517 259,914 269,584 276,159 295,142
225 178,609 183,607 191,281 198,278 206,980 242,631 252,578 260,992 270,681 277,269 296,288
226 179,499 184,510 192,203 199,218 207,940 243,671 253,638 262,070 271,777 278,379 297,433
227 180,390 185,414 193,126 200,158 208,901 244,711 254,699 263,147 272,874 279,488 298,579
228 181,281 186,317 194,049 201,097 209,861 245,750 255,759 264,224 273,970 280,597 299,723
229 182,172 187,221 194,972 202,037 210,822 246,790 256,819 265,301 275,066 281,706 300,868
230 183,063 188,125 195,895 202,978 211,782 247,829 257,879 266,378 276,162 282,814 302,012
231 183,955 189,030 196,818 203,918 212,743 248,868 258,939 267,455 277,258 283,923 303,156
232 184,847 189,934 197,742 204,858 213,704 249,908 259,998 268,531 278,354 285,031 304,299
233 185,739 190,839 198,665 205,799 214,665 250,947 261,058 269,608 279,449 286,139 305,443
234 186,631 191,744 199,589 206,739 215,626 251,986 262,117 270,684 280,544 287,247 306,586
235 187,524 192,649 200,513 207,680 216,587 253,025 263,176 271,760 281,639 288,354 307,728
236 188,417 193,554 201,437 208,621 217,548 254,063 264,235 272,836 282,734 289,461 308,871
237 189,310 194,460 202,362 209,562 218,509 255,102 265,294 273,911 283,828 290,568 310,013


























Dla danej wartości l tapela podaje wartość exp(-l) [do obliczania prawdopodobieństwa w rozkładzie Poissona]














0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,5 2,0

0,90484 0,81873 0,74082 0,67032 0,60653 0,54881 0,49659 0,44933 0,40657 0,36788 0,22313 0,13534

2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 7,0 8,0 9,0 10,0

0,08208 0,04979 0,03020 0,01832 0,01111 0,00674 0,00409 0,00248 0,00091 0,00034 0,00012 0,00005

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