The Poisson Distribution
Cumulative Distribution Function
(PDF)
The columns correspond to different values for the mean ($\mu$) of a
Poisson variable. The entries in the body of the table represent the
probabilities that such a random variable does not exceed the integer
$x$ at the left of the row. For example, a Poisson variable of mean 0.8
is 2 or less with probability 0.953.
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {0.1}& {0.2}& {0.3}& {0.4}&{0.5}&{0.6}&{0.7}&{0.8}&{0.9}&{1.0}\\\hline
\ \\
0&0.905&0.819&0.741&0.670&0.607&0.549&0.497&0.449&0.407&0.368\\
1&0.995&0.982&0.963&0.938&0.910&0.878&0.844&0.809&0.772&0.736\\
2&1.000&0.999&0.996&0.992&0.986&0.977&0.966&0.953&0.937&0.920\\
3&1.000&1.000&1.000&0.999&0.998&0.997&0.994&0.991&0.987&0.981\\
4&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.999&0.998&0.996\\
5&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&0.999\\
6&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000\\
\ \\
&&&&&\mu&&&&&\\
x&{1.1}&{1.2}&{1.3}&{1.4}&{1.5}&{1.6}&{1.7}&{1.8}&{1.9}&{2.0}\\\hline
\ \\
0&0.333&0.301&0.273&0.247&0.223&0.202&0.183&0.165&0.150&0.135\\
1&0.699&0.663&0.627&0.592&0.558&0.525&0.493&0.463&0.434&0.406\\
2&0.900&0.879&0.857&0.833&0.809&0.783&0.757&0.731&0.704&0.677\\
3&0.974&0.966&0.957&0.946&0.934&0.921&0.907&0.891&0.875&0.857\\
4&0.995&0.992&0.989&0.986&0.981&0.976&0.970&0.964&0.956&0.947\\
5&0.999&0.998&0.998&0.997&0.996&0.994&0.992&0.990&0.987&0.983\\
6&1.000&1.000&1.000&0.999&0.999&0.999&0.998&0.997&0.997&0.995\\
7&1.000&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.999&0.999\\
8&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000\\
\ \\
&&&&&\mu&&&&&\\
x&{2.2}&{2.4}&{2.6}&{2.8}&{3.0}&{3.2}&{3.4}&{3.6}&{3.8}&{4.0}\\\hline
\ \\
0&0.111&0.091&0.074&0.061&0.050&0.041&0.033&0.027&0.022&0.018\\
1&0.355&0.308&0.267&0.231&0.199&0.171&0.147&0.126&0.107&0.092\\
2&0.623&0.570&0.518&0.469&0.423&0.380&0.340&0.303&0.269&0.238\\
3&0.819&0.779&0.736&0.692&0.647&0.603&0.558&0.515&0.473&0.433\\
4&0.928&0.904&0.877&0.848&0.815&0.781&0.744&0.706&0.668&0.629\\
5&0.975&0.964&0.951&0.935&0.916&0.895&0.871&0.844&0.816&0.785\\
6&0.993&0.988&0.983&0.976&0.966&0.955&0.942&0.927&0.909&0.889\\
7&0.998&0.997&0.995&0.992&0.988&0.983&0.977&0.969&0.960&0.949\\
8&1.000&0.999&0.999&0.998&0.996&0.994&0.992&0.988&0.984&0.979\\
9&1.000&1.000&1.000&0.999&0.999&0.998&0.997&0.996&0.994&0.992\\
10&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.999&0.998&0.997\\
11&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.999\\
12&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x&
{4.2}&{4.4}&{4.6}&{4.8}&{5.0}&{5.2}&{5.4}&{5.6}&{5.8}&{6.0}\\\hline
\ \\
0&0.015&0.012&0.010&0.008&0.007&0.006&0.005&0.004&0.003&0.002\\
1&0.078&0.066&0.056&0.048&0.040&0.034&0.029&0.024&0.021&0.017\\
2&0.210&0.185&0.163&0.143&0.125&0.109&0.095&0.082&0.072&0.062\\
3&0.395&0.359&0.326&0.294&0.265&0.238&0.213&0.191&0.170&0.151\\
4&0.590&0.551&0.513&0.476&0.440&0.406&0.373&0.342&0.313&0.285\\
5&0.753&0.720&0.686&0.651&0.616&0.581&0.546&0.512&0.478&0.446\\
6&0.867&0.844&0.818&0.791&0.762&0.732&0.702&0.670&0.638&0.606\\
7&0.936&0.921&0.905&0.887&0.867&0.845&0.822&0.797&0.771&0.744\\
8&0.972&0.964&0.955&0.944&0.932&0.918&0.903&0.886&0.867&0.847\\
9&0.989&0.985&0.980&0.975&0.968&0.960&0.951&0.941&0.929&0.916\\
10&0.996&0.994&0.992&0.990&0.986&0.982&0.977&0.972&0.965&0.957\\
11&0.999&0.998&0.997&0.996&0.995&0.993&0.990&0.988&0.984&0.980\\
12&1.000&0.999&0.999&0.999&0.998&0.997&0.996&0.995&0.993&0.991\\
13&1.000&1.000&1.000&1.000&0.999&0.999&0.999&0.998&0.997&0.996\\
14&1.000&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.999&0.999\\
15&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&0.999\\
16&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000\\
\ \\ \\
&&&&&\mu&&&&&\\
x&
{6.5}&{7.0}&{7.5}&{8.0}&{8.5}&{9.0}&{9.5}&{10.0}&{10.5}&{11.0}\\\hline
\ \\
0&0.002&0.001&0.001&0.000&0.000&0.000&0.000&0.000&0.000&0.000\\
1&0.011&0.007&0.005&0.003&0.002&0.001&0.001&0.000&0.000&0.000\\
2&0.043&0.030&0.020&0.014&0.009&0.006&0.004&0.003&0.002&0.001\\
3&0.112&0.082&0.059&0.042&0.030&0.021&0.015&0.010&0.007&0.005\\
4&0.224&0.173&0.132&0.100&0.074&0.055&0.040&0.029&0.021&0.015\\
5&0.369&0.301&0.241&0.191&0.150&0.116&0.089&0.067&0.050&0.038\\
6&0.527&0.450&0.378&0.313&0.256&0.207&0.165&0.130&0.102&0.079\\
7&0.673&0.599&0.525&0.453&0.386&0.324&0.269&0.220&0.179&0.143\\
8&0.792&0.729&0.662&0.593&0.523&0.456&0.392&0.333&0.279&0.232\\
9&0.877&0.830&0.776&0.717&0.653&0.587&0.522&0.458&0.397&0.341\\
10&0.933&0.901&0.862&0.816&0.763&0.706&0.645&0.583&0.521&0.460\\
11&0.966&0.947&0.921&0.888&0.849&0.803&0.752&0.697&0.639&0.579\\
12&0.984&0.973&0.957&0.936&0.909&0.876&0.836&0.792&0.742&0.689\\
13&0.993&0.987&0.978&0.966&0.949&0.926&0.898&0.864&0.825&0.781\\
14&0.997&0.994&0.990&0.983&0.973&0.959&0.940&0.917&0.888&0.854\\
15&0.999&0.998&0.995&0.992&0.986&0.978&0.967&0.951&0.932&0.907\\
16&1.000&0.999&0.998&0.996&0.993&0.989&0.982&0.973&0.960&0.944\\
17&1.000&1.000&0.999&0.998&0.997&0.995&0.991&0.986&0.978&0.968\\
18&1.000&1.000&1.000&0.999&0.999&0.998&0.996&0.993&0.988&0.982\\
19&1.000&1.000&1.000&1.000&0.999&0.999&0.998&0.997&0.994&0.991\\
20&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.998&0.997&0.995\\
21&1.000&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.999&0.998\\
22&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&0.999&0.999\\
23&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000
\end{array}
$$
