Tables of Poisson Cumulative Distribution
The following tables provide the Cumulative Distribution Function (CDF) for a Poisson random variable \( X \). For a given mean = \( \lambda \), each cell represents the probability that the number of events \( X \) is less than or equal to a specific value \( x \).
Table 1: Cumulative Poisson Probabilities (λ = 0.1 to 1.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | |
| 0 | 0.9048 | 0.8187 | 0.7408 | 0.6703 | 0.6065 | 0.5488 | 0.4966 | 0.4493 | 0.4066 | 0.3679 |
| 1 | 0.9953 | 0.9825 | 0.9631 | 0.9384 | 0.9098 | 0.8781 | 0.8442 | 0.8088 | 0.7725 | 0.7358 |
| 2 | 0.9998 | 0.9989 | 0.9964 | 0.9921 | 0.9856 | 0.9769 | 0.9659 | 0.9526 | 0.9371 | 0.9197 |
| 3 | 1.0000 | 0.9999 | 0.9997 | 0.9992 | 0.9982 | 0.9966 | 0.9942 | 0.9909 | 0.9865 | 0.9810 |
| 4 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9996 | 0.9992 | 0.9986 | 0.9977 | 0.9963 |
| 5 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9997 | 0.9994 |
| 6 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 |
| 7 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 8 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 9 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 10 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
Table 2: Cumulative Poisson Probabilities (λ = 1.1 to 2.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | 1.7 | 1.8 | 1.9 | 2.0 | |
| 0 | 0.3329 | 0.3012 | 0.2725 | 0.2466 | 0.2231 | 0.2019 | 0.1827 | 0.1653 | 0.1496 | 0.1353 |
| 1 | 0.6990 | 0.6626 | 0.6268 | 0.5918 | 0.5578 | 0.5249 | 0.4932 | 0.4628 | 0.4337 | 0.4060 |
| 2 | 0.9004 | 0.8795 | 0.8571 | 0.8335 | 0.8088 | 0.7834 | 0.7572 | 0.7306 | 0.7037 | 0.6767 |
| 3 | 0.9743 | 0.9662 | 0.9569 | 0.9463 | 0.9344 | 0.9212 | 0.9068 | 0.8913 | 0.8747 | 0.8571 |
| 4 | 0.9946 | 0.9923 | 0.9893 | 0.9857 | 0.9814 | 0.9763 | 0.9704 | 0.9636 | 0.9559 | 0.9473 |
| 5 | 0.9990 | 0.9985 | 0.9978 | 0.9968 | 0.9955 | 0.9940 | 0.9920 | 0.9896 | 0.9868 | 0.9834 |
| 6 | 0.9999 | 0.9997 | 0.9996 | 0.9994 | 0.9991 | 0.9987 | 0.9981 | 0.9974 | 0.9966 | 0.9955 |
| 7 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9998 | 0.9997 | 0.9996 | 0.9994 | 0.9992 | 0.9989 |
| 8 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9998 | 0.9998 |
| 9 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 10 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
Table 3: Cumulative Poisson Probabilities (λ = 2.1 to 3.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 | 3.0 | |
| 0 | 0.1225 | 0.1108 | 0.1003 | 0.0907 | 0.0821 | 0.0743 | 0.0672 | 0.0608 | 0.0550 | 0.0498 |
| 1 | 0.3796 | 0.3546 | 0.3309 | 0.3084 | 0.2873 | 0.2674 | 0.2487 | 0.2311 | 0.2146 | 0.1991 |
| 2 | 0.6496 | 0.6227 | 0.5960 | 0.5697 | 0.5438 | 0.5184 | 0.4936 | 0.4695 | 0.4460 | 0.4232 |
| 3 | 0.8386 | 0.8194 | 0.7993 | 0.7787 | 0.7576 | 0.7360 | 0.7141 | 0.6919 | 0.6696 | 0.6472 |
| 4 | 0.9379 | 0.9275 | 0.9162 | 0.9041 | 0.8912 | 0.8774 | 0.8629 | 0.8477 | 0.8318 | 0.8153 |
| 5 | 0.9796 | 0.9751 | 0.9700 | 0.9643 | 0.9580 | 0.9510 | 0.9433 | 0.9349 | 0.9258 | 0.9161 |
| 6 | 0.9941 | 0.9925 | 0.9906 | 0.9884 | 0.9858 | 0.9828 | 0.9794 | 0.9756 | 0.9713 | 0.9665 |
| 7 | 0.9985 | 0.9980 | 0.9974 | 0.9967 | 0.9958 | 0.9947 | 0.9934 | 0.9919 | 0.9901 | 0.9881 |
| 8 | 0.9997 | 0.9995 | 0.9994 | 0.9991 | 0.9989 | 0.9985 | 0.9981 | 0.9976 | 0.9969 | 0.9962 |
| 9 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9997 | 0.9996 | 0.9995 | 0.9993 | 0.9991 | 0.9989 |
| 10 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9997 |
Table 4: Cumulative Poisson Probabilities (λ = 3.1 to 4.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 4.0 | |
| 0 | 0.0450 | 0.0408 | 0.0369 | 0.0334 | 0.0302 | 0.0273 | 0.0247 | 0.0224 | 0.0202 | 0.0183 |
| 1 | 0.1847 | 0.1712 | 0.1586 | 0.1468 | 0.1359 | 0.1257 | 0.1162 | 0.1074 | 0.0992 | 0.0916 |
| 2 | 0.4012 | 0.3799 | 0.3594 | 0.3397 | 0.3208 | 0.3027 | 0.2854 | 0.2689 | 0.2531 | 0.2381 |
| 3 | 0.6248 | 0.6025 | 0.5803 | 0.5584 | 0.5366 | 0.5152 | 0.4942 | 0.4735 | 0.4532 | 0.4335 |
| 4 | 0.7982 | 0.7806 | 0.7626 | 0.7442 | 0.7254 | 0.7064 | 0.6872 | 0.6678 | 0.6484 | 0.6288 |
| 5 | 0.9057 | 0.8946 | 0.8829 | 0.8705 | 0.8576 | 0.8441 | 0.8301 | 0.8156 | 0.8006 | 0.7851 |
| 6 | 0.9612 | 0.9554 | 0.9490 | 0.9421 | 0.9347 | 0.9267 | 0.9182 | 0.9091 | 0.8995 | 0.8893 |
| 7 | 0.9858 | 0.9832 | 0.9802 | 0.9769 | 0.9733 | 0.9692 | 0.9648 | 0.9599 | 0.9546 | 0.9489 |
| 8 | 0.9953 | 0.9943 | 0.9931 | 0.9917 | 0.9901 | 0.9883 | 0.9863 | 0.9840 | 0.9815 | 0.9786 |
| 9 | 0.9986 | 0.9982 | 0.9978 | 0.9973 | 0.9967 | 0.9960 | 0.9952 | 0.9942 | 0.9931 | 0.9919 |
| 10 | 0.9996 | 0.9995 | 0.9994 | 0.9992 | 0.9990 | 0.9987 | 0.9984 | 0.9981 | 0.9977 | 0.9972 |
Table 5: Cumulative Poisson Probabilities (λ = 4.1 to 5.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6 | 4.7 | 4.8 | 4.9 | 5.0 | |
| 0 | 0.0166 | 0.0150 | 0.0136 | 0.0123 | 0.0111 | 0.0101 | 0.0091 | 0.0082 | 0.0074 | 0.0067 |
| 1 | 0.0845 | 0.0780 | 0.0719 | 0.0663 | 0.0611 | 0.0563 | 0.0518 | 0.0477 | 0.0439 | 0.0404 |
| 2 | 0.2238 | 0.2102 | 0.1974 | 0.1851 | 0.1736 | 0.1626 | 0.1523 | 0.1425 | 0.1333 | 0.1247 |
| 3 | 0.4142 | 0.3954 | 0.3772 | 0.3594 | 0.3423 | 0.3257 | 0.3097 | 0.2942 | 0.2793 | 0.2650 |
| 4 | 0.6093 | 0.5898 | 0.5704 | 0.5512 | 0.5321 | 0.5132 | 0.4946 | 0.4763 | 0.4582 | 0.4405 |
| 5 | 0.7693 | 0.7531 | 0.7367 | 0.7199 | 0.7029 | 0.6858 | 0.6684 | 0.6510 | 0.6335 | 0.6160 |
| 6 | 0.8786 | 0.8675 | 0.8558 | 0.8436 | 0.8311 | 0.8180 | 0.8046 | 0.7908 | 0.7767 | 0.7622 |
| 7 | 0.9427 | 0.9361 | 0.9290 | 0.9214 | 0.9134 | 0.9049 | 0.8960 | 0.8867 | 0.8769 | 0.8666 |
| 8 | 0.9755 | 0.9721 | 0.9683 | 0.9642 | 0.9597 | 0.9549 | 0.9497 | 0.9442 | 0.9382 | 0.9319 |
| 9 | 0.9905 | 0.9889 | 0.9871 | 0.9851 | 0.9829 | 0.9805 | 0.9778 | 0.9749 | 0.9717 | 0.9682 |
| 10 | 0.9966 | 0.9959 | 0.9952 | 0.9943 | 0.9933 | 0.9922 | 0.9910 | 0.9896 | 0.9880 | 0.9863 |
| 11 | 0.9989 | 0.9986 | 0.9983 | 0.9980 | 0.9976 | 0.9971 | 0.9966 | 0.9960 | 0.9953 | 0.9945 |
| 12 | 0.9997 | 0.9996 | 0.9995 | 0.9993 | 0.9992 | 0.9990 | 0.9988 | 0.9986 | 0.9983 | 0.9980 |
Table 6: Cumulative Poisson Probabilities (λ = 5.1 to 6.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 5.1 | 5.2 | 5.3 | 5.4 | 5.5 | 5.6 | 5.7 | 5.8 | 5.9 | 6.0 | |
| 0 | 0.0061 | 0.0055 | 0.0050 | 0.0045 | 0.0041 | 0.0037 | 0.0033 | 0.0030 | 0.0027 | 0.0025 |
| 1 | 0.0372 | 0.0342 | 0.0314 | 0.0289 | 0.0266 | 0.0244 | 0.0224 | 0.0206 | 0.0189 | 0.0174 |
| 2 | 0.1165 | 0.1088 | 0.1016 | 0.0948 | 0.0884 | 0.0824 | 0.0768 | 0.0715 | 0.0666 | 0.0620 |
| 3 | 0.2513 | 0.2381 | 0.2254 | 0.2133 | 0.2017 | 0.1906 | 0.1800 | 0.1700 | 0.1604 | 0.1512 |
| 4 | 0.4231 | 0.4061 | 0.3895 | 0.3733 | 0.3575 | 0.3422 | 0.3272 | 0.3127 | 0.2987 | 0.2851 |
| 5 | 0.5984 | 0.5809 | 0.5635 | 0.5461 | 0.5289 | 0.5119 | 0.4950 | 0.4783 | 0.4619 | 0.4457 |
| 6 | 0.7474 | 0.7324 | 0.7171 | 0.7017 | 0.6860 | 0.6703 | 0.6544 | 0.6384 | 0.6224 | 0.6063 |
| 7 | 0.8560 | 0.8449 | 0.8335 | 0.8217 | 0.8095 | 0.7970 | 0.7841 | 0.7710 | 0.7576 | 0.7440 |
| 8 | 0.9252 | 0.9181 | 0.9106 | 0.9027 | 0.8944 | 0.8857 | 0.8766 | 0.8672 | 0.8574 | 0.8472 |
| 9 | 0.9644 | 0.9603 | 0.9559 | 0.9512 | 0.9462 | 0.9409 | 0.9352 | 0.9292 | 0.9228 | 0.9161 |
| 10 | 0.9844 | 0.9823 | 0.9800 | 0.9775 | 0.9747 | 0.9718 | 0.9686 | 0.9651 | 0.9614 | 0.9574 |
| 11 | 0.9937 | 0.9927 | 0.9916 | 0.9904 | 0.9890 | 0.9875 | 0.9859 | 0.9841 | 0.9821 | 0.9799 |
| 12 | 0.9976 | 0.9972 | 0.9967 | 0.9962 | 0.9955 | 0.9949 | 0.9941 | 0.9932 | 0.9922 | 0.9912 |
| 13 | 0.9992 | 0.9990 | 0.9988 | 0.9986 | 0.9983 | 0.9980 | 0.9977 | 0.9973 | 0.9969 | 0.9964 |
| 14 | 0.9997 | 0.9997 | 0.9996 | 0.9995 | 0.9994 | 0.9993 | 0.9991 | 0.9990 | 0.9988 | 0.9986 |
| 15 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9998 | 0.9997 | 0.9996 | 0.9996 | 0.9995 |
Table 7: Cumulative Poisson Probabilities (λ = 6.1 to 7.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 6.1 | 6.2 | 6.3 | 6.4 | 6.5 | 6.6 | 6.7 | 6.8 | 6.9 | 7.0 | |
| 0 | 0.0022 | 0.0020 | 0.0018 | 0.0017 | 0.0015 | 0.0014 | 0.0012 | 0.0011 | 0.0010 | 0.0009 |
| 1 | 0.0159 | 0.0146 | 0.0134 | 0.0123 | 0.0113 | 0.0103 | 0.0095 | 0.0087 | 0.0080 | 0.0073 |
| 2 | 0.0577 | 0.0536 | 0.0498 | 0.0463 | 0.0430 | 0.0400 | 0.0371 | 0.0344 | 0.0320 | 0.0296 |
| 3 | 0.1425 | 0.1342 | 0.1264 | 0.1189 | 0.1118 | 0.1052 | 0.0988 | 0.0928 | 0.0871 | 0.0818 |
| 4 | 0.2719 | 0.2592 | 0.2469 | 0.2351 | 0.2237 | 0.2127 | 0.2022 | 0.1920 | 0.1823 | 0.1730 |
| 5 | 0.4298 | 0.4141 | 0.3988 | 0.3837 | 0.3690 | 0.3547 | 0.3406 | 0.3270 | 0.3137 | 0.3007 |
| 6 | 0.5902 | 0.5742 | 0.5582 | 0.5423 | 0.5265 | 0.5108 | 0.4953 | 0.4799 | 0.4647 | 0.4497 |
| 7 | 0.7301 | 0.7160 | 0.7017 | 0.6873 | 0.6728 | 0.6581 | 0.6433 | 0.6285 | 0.6136 | 0.5987 |
| 8 | 0.8367 | 0.8259 | 0.8148 | 0.8033 | 0.7916 | 0.7796 | 0.7673 | 0.7548 | 0.7420 | 0.7291 |
| 9 | 0.9090 | 0.9016 | 0.8939 | 0.8858 | 0.8774 | 0.8686 | 0.8596 | 0.8502 | 0.8405 | 0.8305 |
| 10 | 0.9531 | 0.9486 | 0.9437 | 0.9386 | 0.9332 | 0.9274 | 0.9214 | 0.9151 | 0.9084 | 0.9015 |
| 11 | 0.9776 | 0.9750 | 0.9723 | 0.9693 | 0.9661 | 0.9627 | 0.9591 | 0.9552 | 0.9510 | 0.9467 |
| 12 | 0.9900 | 0.9887 | 0.9873 | 0.9857 | 0.9840 | 0.9821 | 0.9801 | 0.9779 | 0.9755 | 0.9730 |
| 13 | 0.9958 | 0.9952 | 0.9945 | 0.9937 | 0.9929 | 0.9920 | 0.9909 | 0.9898 | 0.9885 | 0.9872 |
| 14 | 0.9984 | 0.9981 | 0.9978 | 0.9974 | 0.9970 | 0.9966 | 0.9961 | 0.9956 | 0.9950 | 0.9943 |
| 15 | 0.9994 | 0.9993 | 0.9992 | 0.9990 | 0.9988 | 0.9986 | 0.9984 | 0.9982 | 0.9979 | 0.9976 |
| 16 | 0.9998 | 0.9997 | 0.9997 | 0.9996 | 0.9996 | 0.9995 | 0.9994 | 0.9993 | 0.9992 | 0.9990 |
| 17 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9998 | 0.9997 | 0.9997 | 0.9996 |
Table 8: Cumulative Poisson Probabilities (λ = 7.1 to 8.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 7.1 | 7.2 | 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 8.0 | |
| 0 | 0.0008 | 0.0007 | 0.0007 | 0.0006 | 0.0006 | 0.0005 | 0.0005 | 0.0004 | 0.0004 | 0.0003 |
| 1 | 0.0067 | 0.0061 | 0.0056 | 0.0051 | 0.0047 | 0.0043 | 0.0039 | 0.0036 | 0.0033 | 0.0030 |
| 2 | 0.0275 | 0.0255 | 0.0236 | 0.0219 | 0.0203 | 0.0188 | 0.0174 | 0.0161 | 0.0149 | 0.0138 |
| 3 | 0.0767 | 0.0719 | 0.0674 | 0.0632 | 0.0591 | 0.0554 | 0.0518 | 0.0485 | 0.0453 | 0.0424 |
| 4 | 0.1641 | 0.1555 | 0.1473 | 0.1395 | 0.1321 | 0.1249 | 0.1181 | 0.1117 | 0.1055 | 0.0996 |
| 5 | 0.2881 | 0.2759 | 0.2640 | 0.2526 | 0.2414 | 0.2307 | 0.2203 | 0.2103 | 0.2006 | 0.1912 |
| 6 | 0.4349 | 0.4204 | 0.4060 | 0.3920 | 0.3782 | 0.3646 | 0.3514 | 0.3384 | 0.3257 | 0.3134 |
| 7 | 0.5838 | 0.5689 | 0.5541 | 0.5393 | 0.5246 | 0.5100 | 0.4956 | 0.4812 | 0.4670 | 0.4530 |
| 8 | 0.7160 | 0.7027 | 0.6892 | 0.6757 | 0.6620 | 0.6482 | 0.6343 | 0.6204 | 0.6065 | 0.5925 |
| 9 | 0.8202 | 0.8096 | 0.7988 | 0.7877 | 0.7764 | 0.7649 | 0.7531 | 0.7411 | 0.7290 | 0.7166 |
| 10 | 0.8942 | 0.8867 | 0.8788 | 0.8707 | 0.8622 | 0.8535 | 0.8445 | 0.8352 | 0.8257 | 0.8159 |
| 11 | 0.9420 | 0.9371 | 0.9319 | 0.9265 | 0.9208 | 0.9148 | 0.9085 | 0.9020 | 0.8952 | 0.8881 |
| 12 | 0.9703 | 0.9673 | 0.9642 | 0.9609 | 0.9573 | 0.9536 | 0.9496 | 0.9454 | 0.9409 | 0.9362 |
| 13 | 0.9857 | 0.9841 | 0.9824 | 0.9805 | 0.9784 | 0.9762 | 0.9739 | 0.9714 | 0.9687 | 0.9658 |
| 14 | 0.9935 | 0.9927 | 0.9918 | 0.9908 | 0.9897 | 0.9886 | 0.9873 | 0.9859 | 0.9844 | 0.9827 |
| 15 | 0.9972 | 0.9969 | 0.9964 | 0.9959 | 0.9954 | 0.9948 | 0.9941 | 0.9934 | 0.9926 | 0.9918 |
| 16 | 0.9989 | 0.9987 | 0.9985 | 0.9983 | 0.9980 | 0.9978 | 0.9974 | 0.9971 | 0.9967 | 0.9963 |
| 17 | 0.9996 | 0.9995 | 0.9994 | 0.9993 | 0.9992 | 0.9991 | 0.9989 | 0.9988 | 0.9986 | 0.9984 |
| 18 | 0.9998 | 0.9998 | 0.9998 | 0.9997 | 0.9997 | 0.9996 | 0.9996 | 0.9995 | 0.9994 | 0.9993 |
| 19 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9998 | 0.9997 |
| 20 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9999 | 0.9999 |
Table 9: Cumulative Poisson Probabilities (λ = 8.1 to 9.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.6 | 8.7 | 8.8 | 8.9 | 9.0 | |
| 0 | 0.0003 | 0.0003 | 0.0002 | 0.0002 | 0.0002 | 0.0002 | 0.0002 | 0.0002 | 0.0001 | 0.0001 |
| 1 | 0.0028 | 0.0025 | 0.0023 | 0.0021 | 0.0019 | 0.0018 | 0.0016 | 0.0015 | 0.0014 | 0.0012 |
| 2 | 0.0127 | 0.0118 | 0.0109 | 0.0100 | 0.0093 | 0.0086 | 0.0079 | 0.0073 | 0.0068 | 0.0062 |
| 3 | 0.0396 | 0.0370 | 0.0346 | 0.0323 | 0.0301 | 0.0281 | 0.0262 | 0.0244 | 0.0228 | 0.0212 |
| 4 | 0.0940 | 0.0887 | 0.0837 | 0.0789 | 0.0744 | 0.0701 | 0.0660 | 0.0621 | 0.0584 | 0.0550 |
| 5 | 0.1822 | 0.1736 | 0.1653 | 0.1573 | 0.1496 | 0.1422 | 0.1352 | 0.1284 | 0.1219 | 0.1157 |
| 6 | 0.3013 | 0.2896 | 0.2781 | 0.2670 | 0.2562 | 0.2457 | 0.2355 | 0.2256 | 0.2160 | 0.2068 |
| 7 | 0.4391 | 0.4254 | 0.4119 | 0.3987 | 0.3856 | 0.3728 | 0.3602 | 0.3478 | 0.3357 | 0.3239 |
| 8 | 0.5786 | 0.5647 | 0.5507 | 0.5369 | 0.5231 | 0.5094 | 0.4958 | 0.4823 | 0.4689 | 0.4557 |
| 9 | 0.7041 | 0.6915 | 0.6788 | 0.6659 | 0.6530 | 0.6400 | 0.6269 | 0.6137 | 0.6006 | 0.5874 |
| 10 | 0.8058 | 0.7955 | 0.7850 | 0.7743 | 0.7634 | 0.7522 | 0.7409 | 0.7294 | 0.7178 | 0.7060 |
| 11 | 0.8807 | 0.8731 | 0.8652 | 0.8571 | 0.8487 | 0.8400 | 0.8311 | 0.8220 | 0.8126 | 0.8030 |
| 12 | 0.9313 | 0.9261 | 0.9207 | 0.9150 | 0.9091 | 0.9029 | 0.8965 | 0.8898 | 0.8829 | 0.8758 |
| 13 | 0.9628 | 0.9595 | 0.9561 | 0.9524 | 0.9486 | 0.9445 | 0.9403 | 0.9358 | 0.9311 | 0.9261 |
| 14 | 0.9810 | 0.9791 | 0.9771 | 0.9749 | 0.9726 | 0.9701 | 0.9675 | 0.9647 | 0.9617 | 0.9585 |
| 15 | 0.9908 | 0.9898 | 0.9887 | 0.9875 | 0.9862 | 0.9848 | 0.9832 | 0.9816 | 0.9798 | 0.9780 |
| 16 | 0.9958 | 0.9953 | 0.9947 | 0.9941 | 0.9934 | 0.9926 | 0.9918 | 0.9909 | 0.9899 | 0.9889 |
| 17 | 0.9982 | 0.9979 | 0.9977 | 0.9973 | 0.9970 | 0.9966 | 0.9962 | 0.9957 | 0.9952 | 0.9947 |
| 18 | 0.9992 | 0.9991 | 0.9990 | 0.9989 | 0.9987 | 0.9985 | 0.9983 | 0.9981 | 0.9978 | 0.9976 |
| 19 | 0.9997 | 0.9997 | 0.9996 | 0.9995 | 0.9995 | 0.9994 | 0.9993 | 0.9992 | 0.9991 | 0.9989 |
| 20 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9998 | 0.9998 | 0.9997 | 0.9997 | 0.9996 | 0.9996 |
| 21 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 |
| 22 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 |
Table 10: Cumulative Poisson Probabilities (λ = 9.1 to 10.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 9.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.8 | 9.9 | 10.0 | |
| 0 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0000 |
| 1 | 0.0011 | 0.0010 | 0.0009 | 0.0009 | 0.0008 | 0.0007 | 0.0007 | 0.0006 | 0.0005 | 0.0005 |
| 2 | 0.0058 | 0.0053 | 0.0049 | 0.0045 | 0.0042 | 0.0038 | 0.0035 | 0.0033 | 0.0030 | 0.0028 |
| 3 | 0.0198 | 0.0184 | 0.0172 | 0.0160 | 0.0149 | 0.0138 | 0.0129 | 0.0120 | 0.0111 | 0.0103 |
| 4 | 0.0517 | 0.0486 | 0.0456 | 0.0429 | 0.0403 | 0.0378 | 0.0355 | 0.0333 | 0.0312 | 0.0293 |
| 5 | 0.1098 | 0.1041 | 0.0986 | 0.0935 | 0.0885 | 0.0838 | 0.0793 | 0.0750 | 0.0710 | 0.0671 |
| 6 | 0.1978 | 0.1892 | 0.1808 | 0.1727 | 0.1649 | 0.1574 | 0.1502 | 0.1433 | 0.1366 | 0.1301 |
| 7 | 0.3123 | 0.3010 | 0.2900 | 0.2792 | 0.2687 | 0.2584 | 0.2485 | 0.2388 | 0.2294 | 0.2202 |
| 8 | 0.4426 | 0.4296 | 0.4168 | 0.4042 | 0.3918 | 0.3796 | 0.3676 | 0.3558 | 0.3442 | 0.3328 |
| 9 | 0.5742 | 0.5611 | 0.5479 | 0.5349 | 0.5218 | 0.5089 | 0.4960 | 0.4832 | 0.4705 | 0.4579 |
| 10 | 0.6941 | 0.6820 | 0.6699 | 0.6576 | 0.6453 | 0.6329 | 0.6205 | 0.6080 | 0.5955 | 0.5830 |
| 11 | 0.7932 | 0.7832 | 0.7730 | 0.7626 | 0.7520 | 0.7412 | 0.7303 | 0.7193 | 0.7081 | 0.6968 |
| 12 | 0.8684 | 0.8607 | 0.8529 | 0.8448 | 0.8364 | 0.8279 | 0.8191 | 0.8101 | 0.8009 | 0.7916 |
| 13 | 0.9210 | 0.9156 | 0.9100 | 0.9042 | 0.8981 | 0.8919 | 0.8853 | 0.8786 | 0.8716 | 0.8645 |
| 14 | 0.9552 | 0.9517 | 0.9480 | 0.9441 | 0.9400 | 0.9357 | 0.9312 | 0.9265 | 0.9216 | 0.9165 |
| 15 | 0.9760 | 0.9738 | 0.9715 | 0.9691 | 0.9665 | 0.9638 | 0.9609 | 0.9579 | 0.9546 | 0.9513 |
| 16 | 0.9878 | 0.9865 | 0.9852 | 0.9838 | 0.9823 | 0.9806 | 0.9789 | 0.9770 | 0.9751 | 0.9730 |
| 17 | 0.9941 | 0.9934 | 0.9927 | 0.9919 | 0.9911 | 0.9902 | 0.9892 | 0.9881 | 0.9870 | 0.9857 |
| 18 | 0.9973 | 0.9969 | 0.9966 | 0.9962 | 0.9957 | 0.9952 | 0.9947 | 0.9941 | 0.9935 | 0.9928 |
| 19 | 0.9988 | 0.9986 | 0.9985 | 0.9983 | 0.9980 | 0.9978 | 0.9975 | 0.9972 | 0.9969 | 0.9965 |
| 20 | 0.9995 | 0.9994 | 0.9993 | 0.9992 | 0.9991 | 0.9990 | 0.9989 | 0.9987 | 0.9986 | 0.9984 |
| 21 | 0.9998 | 0.9998 | 0.9997 | 0.9997 | 0.9996 | 0.9996 | 0.9995 | 0.9995 | 0.9994 | 0.9993 |
| 22 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9998 | 0.9997 | 0.9997 |
| 23 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 |
| 24 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 25 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
Table 11: Cumulative Poisson Probabilities (λ = 10.1 to 11.0)
| x | Mean (λ) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 10.1 | 10.2 | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | 10.9 | 11.0 | |
| 0 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
| 1 | 0.0005 | 0.0004 | 0.0004 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0002 | 0.0002 | 0.0002 |
| 2 | 0.0026 | 0.0023 | 0.0022 | 0.0020 | 0.0018 | 0.0017 | 0.0016 | 0.0014 | 0.0013 | 0.0012 |
| 3 | 0.0096 | 0.0089 | 0.0083 | 0.0077 | 0.0071 | 0.0066 | 0.0062 | 0.0057 | 0.0053 | 0.0049 |
| 4 | 0.0274 | 0.0257 | 0.0241 | 0.0225 | 0.0211 | 0.0197 | 0.0185 | 0.0173 | 0.0162 | 0.0151 |
| 5 | 0.0634 | 0.0599 | 0.0566 | 0.0534 | 0.0504 | 0.0475 | 0.0448 | 0.0423 | 0.0398 | 0.0375 |
| 6 | 0.1240 | 0.1180 | 0.1123 | 0.1069 | 0.1016 | 0.0966 | 0.0918 | 0.0872 | 0.0828 | 0.0786 |
| 7 | 0.2113 | 0.2027 | 0.1944 | 0.1863 | 0.1785 | 0.1710 | 0.1636 | 0.1566 | 0.1498 | 0.1432 |
| 8 | 0.3217 | 0.3108 | 0.3001 | 0.2896 | 0.2794 | 0.2694 | 0.2597 | 0.2502 | 0.2410 | 0.2320 |
| 9 | 0.4455 | 0.4332 | 0.4210 | 0.4090 | 0.3971 | 0.3854 | 0.3739 | 0.3626 | 0.3515 | 0.3405 |
| 10 | 0.5705 | 0.5580 | 0.5456 | 0.5331 | 0.5207 | 0.5084 | 0.4961 | 0.4840 | 0.4719 | 0.4599 |
| 11 | 0.6853 | 0.6738 | 0.6622 | 0.6505 | 0.6387 | 0.6269 | 0.6150 | 0.6031 | 0.5912 | 0.5793 |
| 12 | 0.7820 | 0.7722 | 0.7623 | 0.7522 | 0.7420 | 0.7316 | 0.7210 | 0.7104 | 0.6996 | 0.6887 |
| 13 | 0.8571 | 0.8494 | 0.8416 | 0.8336 | 0.8253 | 0.8169 | 0.8083 | 0.7995 | 0.7905 | 0.7813 |
| 14 | 0.9112 | 0.9057 | 0.9000 | 0.8940 | 0.8879 | 0.8815 | 0.8750 | 0.8682 | 0.8612 | 0.8540 |
| 15 | 0.9477 | 0.9440 | 0.9400 | 0.9359 | 0.9317 | 0.9272 | 0.9225 | 0.9177 | 0.9126 | 0.9074 |
| 16 | 0.9707 | 0.9684 | 0.9658 | 0.9632 | 0.9604 | 0.9574 | 0.9543 | 0.9511 | 0.9477 | 0.9441 |
| 17 | 0.9844 | 0.9830 | 0.9815 | 0.9799 | 0.9781 | 0.9763 | 0.9744 | 0.9723 | 0.9701 | 0.9678 |
| 18 | 0.9921 | 0.9913 | 0.9904 | 0.9895 | 0.9885 | 0.9874 | 0.9863 | 0.9850 | 0.9837 | 0.9823 |
| 19 | 0.9962 | 0.9957 | 0.9953 | 0.9948 | 0.9942 | 0.9936 | 0.9930 | 0.9923 | 0.9915 | 0.9907 |
| 20 | 0.9982 | 0.9980 | 0.9978 | 0.9975 | 0.9972 | 0.9969 | 0.9966 | 0.9962 | 0.9958 | 0.9953 |
| 21 | 0.9992 | 0.9991 | 0.9990 | 0.9989 | 0.9987 | 0.9986 | 0.9984 | 0.9982 | 0.9980 | 0.9977 |
| 22 | 0.9997 | 0.9996 | 0.9996 | 0.9995 | 0.9994 | 0.9994 | 0.9993 | 0.9992 | 0.9991 | 0.9990 |
| 23 | 0.9999 | 0.9998 | 0.9998 | 0.9998 | 0.9998 | 0.9997 | 0.9997 | 0.9996 | 0.9996 | 0.9995 |
| 24 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9998 |
| 25 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9999 | 0.9999 |
| 26 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 27 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
Discussion