The Poisson Distribution
Probability Density 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 equals the integer
$x$ at the left of the row. For example, a Poisson variable of mean 0.3
is 2 with probability 0.2222.
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {0.1}& {0.2}& {0.3}& {0.4}&{0.5}&{0.6}&{0.7}&{0.8}&{0.9}&{1.0}\\\hline
0& 0.9048&0.8187&0.7408&0.6703&0.6065&0.5488&0.4966&0.4493&0.4066&0.3679\\
1& 0.0905&0.1637&0.2222&0.2681&0.3033&0.3293&0.3476&0.3595&0.3659&0.3679\\
2& 0.0045&0.0164&0.0333&0.0536&0.0758&0.0988&0.1217&0.1438&0.1647&0.1839\\
3& 0.0002&0.0011&0.0033&0.0072&0.0126&0.0198&0.0284&0.0383&0.0494&0.0613\\
4& \phantom{0}&0.0001&0.0003&0.0007&0.0016&0.0030&0.0050&0.0077&0.0111&0.0153\\
5& \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0004&0.0007&0.0012&0.0020&0.0031\\
6& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0003&0.0005\\
7& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {1.1}& {1.2}& {1.3}& {1.4}&{1.5}&{1.6}&{1.7}&{1.8}&{1.9}&{2.0}\\\hline
0& 0.3329&0.3012&0.2725&0.2466&0.2231&0.2019&0.1827&0.1653&0.1496&0.1353\\
1& 0.3662&0.3614&0.3543&0.3452&0.3347&0.3230&0.3106&0.2975&0.2842&0.2707\\
2& 0.2014&0.2169&0.2303&0.2417&0.2510&0.2584&0.2640&0.2678&0.2700&0.2707\\
3& 0.0738&0.0867&0.0998&0.1128&0.1255&0.1378&0.1496&0.1607&0.1710&0.1804\\
4& 0.0203&0.0260&0.0324&0.0395&0.0471&0.0551&0.0636&0.0723&0.0812&0.0902\\
5& 0.0045&0.0062&0.0084&0.0111&0.0141&0.0176&0.0216&0.0260&0.0309&0.0361\\
6& 0.0008&0.0012&0.0018&0.0026&0.0035&0.0047&0.0061&0.0078&0.0098&0.0120\\
7& 0.0001&0.0002&0.0003&0.0005&0.0008&0.0011&0.0015&0.0020&0.0027&0.0034\\
8& \phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0002&0.0003&0.0005&0.0006&0.0009\\
9& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0002\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {2.1}& {2.2}& {2.3}& {2.4}&{2.5}&{2.6}&{2.7}&{2.8}&{2.9}&{3.0}\\\hline
0& 0.1225&0.1108&0.1003&0.0907&0.0821&0.0743&0.0672&0.0608&0.0550&0.0498\\
1& 0.2572&0.2438&0.2306&0.2177&0.2052&0.1931&0.1815&0.1703&0.1596&0.1494\\
2& 0.2700&0.2681&0.2652&0.2613&0.2565&0.2510&0.2450&0.2384&0.2314&0.2240\\
3& 0.1890&0.1966&0.2033&0.2090&0.2138&0.2176&0.2205&0.2225&0.2237&0.2240\\
4& 0.0992&0.1082&0.1169&0.1254&0.1336&0.1414&0.1488&0.1557&0.1622&0.1680\\
5& 0.0417&0.0476&0.0538&0.0602&0.0668&0.0735&0.0804&0.0872&0.0940&0.1008\\
6& 0.0146&0.0174&0.0206&0.0241&0.0278&0.0319&0.0362&0.0407&0.0455&0.0504\\
7& 0.0044&0.0055&0.0068&0.0083&0.0099&0.0118&0.0139&0.0163&0.0188&0.0216\\
8& 0.0011&0.0015&0.0019&0.0025&0.0031&0.0038&0.0047&0.0057&0.0068&0.0081\\
9& 0.0003&0.0004&0.0005&0.0007&0.0009&0.0011&0.0014&0.0018&0.0022&0.0027\\
10& 0.0001&0.0001&0.0001&0.0002&0.0002&0.0003&0.0004&0.0005&0.0006&0.0008\\
11& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0002&0.0002\\
12& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {3.1}& {3.2}& {3.3}& {3.4}&{3.5}&{3.6}&{3.7}&{3.8}&{3.9}&{4.0}\\\hline
0& 0.0450&0.0408&0.0369&0.0334&0.0302&0.0273&0.0247&0.0224&0.0202&0.0183\\
1& 0.1397&0.1304&0.1217&0.1135&0.1057&0.0984&0.0915&0.0850&0.0789&0.0733\\
2& 0.2165&0.2087&0.2008&0.1929&0.1850&0.1771&0.1692&0.1615&0.1539&0.1465\\
3& 0.2237&0.2226&0.2209&0.2186&0.2158&0.2125&0.2087&0.2046&0.2001&0.1954\\
4& 0.1733&0.1781&0.1823&0.1858&0.1888&0.1912&0.1931&0.1944&0.1951&0.1954\\
5& 0.1075&0.1140&0.1203&0.1264&0.1322&0.1377&0.1429&0.1477&0.1522&0.1563\\
6& 0.0555&0.0608&0.0662&0.0716&0.0771&0.0826&0.0881&0.0936&0.0989&0.1042\\
7& 0.0246&0.0278&0.0312&0.0348&0.0385&0.0425&0.0466&0.0508&0.0551&0.0595\\
8& 0.0095&0.0111&0.0129&0.0148&0.0169&0.0191&0.0215&0.0241&0.0269&0.0298\\
9& 0.0033&0.0040&0.0047&0.0056&0.0066&0.0076&0.0089&0.0102&0.0116&0.0132\\
10& 0.0010&0.0013&0.0016&0.0019&0.0023&0.0028&0.0033&0.0039&0.0045&0.0053\\
11& 0.0003&0.0004&0.0005&0.0006&0.0007&0.0009&0.0011&0.0013&0.0016&0.0019\\
12& 0.0001&0.0001&0.0001&0.0002&0.0002&0.0003&0.0003&0.0004&0.0005&0.0006\\
13& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0001&0.0002&0.0002\\
14& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {4.1}& {4.2}& {4.3}& {4.4}&{4.5}&{4.6}&{4.7}&{4.8}&{4.9}&{5.0}\\\hline
0& 0.0166&0.0150&0.0136&0.0123&0.0111&0.0101&0.0091&0.0082&0.0074&0.0067\\
1& 0.0679&0.0630&0.0583&0.0540&0.0500&0.0462&0.0427&0.0395&0.0365&0.0337\\
2& 0.1393&0.1323&0.1254&0.1188&0.1125&0.1063&0.1005&0.0948&0.0894&0.0842\\
3& 0.1904&0.1852&0.1798&0.1743&0.1687&0.1631&0.1574&0.1517&0.1460&0.1404\\
4& 0.1951&0.1944&0.1933&0.1917&0.1898&0.1875&0.1849&0.1820&0.1789&0.1755\\
5& 0.1600&0.1633&0.1662&0.1687&0.1708&0.1725&0.1738&0.1747&0.1753&0.1755\\
6& 0.1093&0.1143&0.1191&0.1237&0.1281&0.1323&0.1362&0.1398&0.1432&0.1462\\
7& 0.0640&0.0686&0.0732&0.0778&0.0824&0.0869&0.0914&0.0959&0.1002&0.1044\\
8& 0.0328&0.0360&0.0393&0.0428&0.0463&0.0500&0.0537&0.0575&0.0614&0.0653\\
9& 0.0150&0.0168&0.0188&0.0209&0.0232&0.0255&0.0281&0.0307&0.0334&0.0363\\
10& 0.0061&0.0071&0.0081&0.0092&0.0104&0.0118&0.0132&0.0147&0.0164&0.0181\\
11& 0.0023&0.0027&0.0032&0.0037&0.0043&0.0049&0.0056&0.0064&0.0073&0.0082\\
12& 0.0008&0.0009&0.0011&0.0013&0.0016&0.0019&0.0022&0.0026&0.0030&0.0034\\
13& 0.0002&0.0003&0.0004&0.0005&0.0006&0.0007&0.0008&0.0009&0.0011&0.0013\\
14& 0.0001&0.0001&0.0001&0.0001&0.0002&0.0002&0.0003&0.0003&0.0004&0.0005\\
15& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0001&0.0001&0.0002\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {5.1}& {5.2}& {5.3}& {5.4}&{5.5}&{5.6}&{5.7}&{5.8}&{5.9}&{6.0}\\\hline
1& 0.0061&0.0055&0.0050&0.0045&0.0041&0.0037&0.0033&0.0030&0.0027&0.0025\\
2& 0.0311&0.0287&0.0265&0.0244&0.0225&0.0207&0.0191&0.0176&0.0162&0.0149\\
3& 0.0793&0.0746&0.0701&0.0659&0.0618&0.0580&0.0544&0.0509&0.0477&0.0446\\
4& 0.1348&0.1293&0.1239&0.1185&0.1133&0.1082&0.1033&0.0985&0.0938&0.0892\\
5& 0.1719&0.1681&0.1641&0.1600&0.1558&0.1515&0.1472&0.1428&0.1383&0.1339\\
6& 0.1753&0.1748&0.1740&0.1728&0.1714&0.1697&0.1678&0.1656&0.1632&0.1606\\
7& 0.1490&0.1515&0.1537&0.1555&0.1571&0.1584&0.1594&0.1601&0.1605&0.1606\\
8& 0.1086&0.1125&0.1163&0.1200&0.1234&0.1267&0.1298&0.1326&0.1353&0.1377\\
9& 0.0692&0.0731&0.0771&0.0810&0.0849&0.0887&0.0925&0.0962&0.0998&0.1033\\
10& 0.0392&0.0423&0.0454&0.0486&0.0519&0.0552&0.0586&0.0620&0.0654&0.0688\\
11& 0.0200&0.0220&0.0241&0.0262&0.0285&0.0309&0.0334&0.0359&0.0386&0.0413\\
12& 0.0093&0.0104&0.0116&0.0129&0.0143&0.0157&0.0173&0.0190&0.0207&0.0225\\
13& 0.0039&0.0045&0.0051&0.0058&0.0065&0.0073&0.0082&0.0092&0.0102&0.0113\\
14& 0.0015&0.0018&0.0021&0.0024&0.0028&0.0032&0.0036&0.0041&0.0046&0.0052\\
15& 0.0006&0.0007&0.0008&0.0009&0.0011&0.0013&0.0015&0.0017&0.0019&0.0022\\
16& 0.0002&0.0002&0.0003&0.0003&0.0004&0.0005&0.0006&0.0007&0.0008&0.0009\\
17& 0.0001&0.0001&0.0001&0.0001&0.0001&0.0002&0.0002&0.0002&0.0003&0.0003\\
18& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0001&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {6.1}& {6.2}& {6.3}& {6.4}&{6.5}&{6.6}&{6.7}&{6.8}&{6.9}&{7.0}\\\hline
0& 0.0022&0.0020&0.0018&0.0017&0.0015&0.0014&0.0012&0.0011&0.0010&0.0009\\
1& 0.0137&0.0126&0.0116&0.0106&0.0098&0.0090&0.0082&0.0076&0.0070&0.0064\\
2& 0.0417&0.0390&0.0364&0.0340&0.0318&0.0296&0.0276&0.0258&0.0240&0.0223\\
3& 0.0848&0.0806&0.0765&0.0726&0.0688&0.0652&0.0617&0.0584&0.0552&0.0521\\
4& 0.1294&0.1249&0.1205&0.1162&0.1118&0.1076&0.1034&0.0992&0.0952&0.0912\\
5& 0.1579&0.1549&0.1519&0.1487&0.1454&0.1420&0.1385&0.1349&0.1314&0.1277\\
6& 0.1605&0.1601&0.1595&0.1586&0.1575&0.1562&0.1546&0.1529&0.1511&0.1490\\
7& 0.1399&0.1418&0.1435&0.1450&0.1462&0.1472&0.1480&0.1486&0.1489&0.1490\\
8& 0.1066&0.1099&0.1130&0.1160&0.1188&0.1215&0.1240&0.1263&0.1284&0.1304\\
9& 0.0723&0.0757&0.0791&0.0825&0.0858&0.0891&0.0923&0.0954&0.0985&0.1014\\
10& 0.0441&0.0469&0.0498&0.0528&0.0558&0.0588&0.0618&0.0649&0.0679&0.0710\\
11& 0.0244&0.0265&0.0285&0.0307&0.0330&0.0353&0.0377&0.0401&0.0426&0.0452\\
12& 0.0124&0.0137&0.0150&0.0164&0.0179&0.0194&0.0210&0.0227&0.0245&0.0263\\
13& 0.0058&0.0065&0.0073&0.0081&0.0089&0.0099&0.0108&0.0119&0.0130&0.0142\\
14& 0.0025&0.0029&0.0033&0.0037&0.0041&0.0046&0.0052&0.0058&0.0064&0.0071\\
15& 0.0010&0.0012&0.0014&0.0016&0.0018&0.0020&0.0023&0.0026&0.0029&0.0033\\
16& 0.0004&0.0005&0.0005&0.0006&0.0007&0.0008&0.0010&0.0011&0.0013&0.0014\\
17& 0.0001&0.0002&0.0002&0.0002&0.0003&0.0003&0.0004&0.0004&0.0005&0.0006\\
18& \phantom{0}&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0002&0.0002&0.0002\\
19& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {7.1}& {7.2}& {7.3}& {7.4}&{7.5}&{7.6}&{7.7}&{7.8}&{7.9}&{8.0}\\\hline
0& 0.0008&0.0007&0.0007&0.0006&0.0006&0.0005&0.0005&0.0004&0.0004&0.0003\\
1& 0.0059&0.0054&0.0049&0.0045&0.0041&0.0038&0.0035&0.0032&0.0029&0.0027\\
2& 0.0208&0.0194&0.0180&0.0167&0.0156&0.0145&0.0134&0.0125&0.0116&0.0107\\
3& 0.0492&0.0464&0.0438&0.0413&0.0389&0.0366&0.0345&0.0324&0.0305&0.0286\\
4& 0.0874&0.0836&0.0799&0.0764&0.0729&0.0696&0.0663&0.0632&0.0602&0.0573\\
5& 0.1241&0.1204&0.1167&0.1130&0.1094&0.1057&0.1021&0.0986&0.0951&0.0916\\
6& 0.1468&0.1445&0.1420&0.1394&0.1367&0.1339&0.1311&0.1282&0.1252&0.1221\\
7& 0.1489&0.1486&0.1481&0.1474&0.1465&0.1454&0.1442&0.1428&0.1413&0.1396\\
8& 0.1321&0.1337&0.1351&0.1363&0.1373&0.1381&0.1388&0.1392&0.1395&0.1396\\
9& 0.1042&0.1070&0.1096&0.1121&0.1144&0.1167&0.1187&0.1207&0.1224&0.1241\\
10& 0.0740&0.0770&0.0800&0.0829&0.0858&0.0887&0.0914&0.0941&0.0967&0.0993\\
11& 0.0478&0.0504&0.0531&0.0558&0.0585&0.0613&0.0640&0.0667&0.0695&0.0722\\
12& 0.0283&0.0303&0.0323&0.0344&0.0366&0.0388&0.0411&0.0434&0.0457&0.0481\\
13& 0.0154&0.0168&0.0181&0.0196&0.0211&0.0227&0.0243&0.0260&0.0278&0.0296\\
14& 0.0078&0.0086&0.0095&0.0104&0.0113&0.0123&0.0134&0.0145&0.0157&0.0169\\
15& 0.0037&0.0041&0.0046&0.0051&0.0057&0.0062&0.0069&0.0075&0.0083&0.0090\\
16& 0.0016&0.0019&0.0021&0.0024&0.0026&0.0030&0.0033&0.0037&0.0041&0.0045\\
17& 0.0007&0.0008&0.0009&0.0010&0.0012&0.0013&0.0015&0.0017&0.0019&0.0021\\
18& 0.0003&0.0003&0.0004&0.0004&0.0005&0.0006&0.0006&0.0007&0.0008&0.0009\\
19& 0.0001&0.0001&0.0001&0.0002&0.0002&0.0002&0.0003&0.0003&0.0003&0.0004\\
20& \phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0002\\
21& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {8.1}& {8.2}& {8.3}& {8.4}&{8.5}&{8.6}&{8.7}&{8.8}&{8.9}&{9.0}\\\hline
0& 0.0003&0.0003&0.0002&0.0002&0.0002&0.0002&0.0002&0.0002&0.0001&0.0001\\
1& 0.0025&0.0023&0.0021&0.0019&0.0017&0.0016&0.0014&0.0013&0.0012&0.0011\\
2& 0.0100&0.0092&0.0086&0.0079&0.0074&0.0068&0.0063&0.0058&0.0054&0.0050\\
3& 0.0269&0.0252&0.0237&0.0222&0.0208&0.0195&0.0183&0.0171&0.0160&0.0150\\
4& 0.0544&0.0517&0.0491&0.0466&0.0443&0.0420&0.0398&0.0377&0.0357&0.0337\\
5& 0.0882&0.0849&0.0816&0.0784&0.0752&0.0722&0.0692&0.0663&0.0635&0.0607\\
6& 0.1191&0.1160&0.1128&0.1097&0.1066&0.1034&0.1003&0.0972&0.0941&0.0911\\
7& 0.1378&0.1358&0.1338&0.1317&0.1294&0.1271&0.1247&0.1222&0.1197&0.1171\\
8& 0.1395&0.1392&0.1388&0.1382&0.1375&0.1366&0.1356&0.1344&0.1332&0.1318\\
9& 0.1256&0.1269&0.1280&0.1290&0.1299&0.1306&0.1311&0.1315&0.1317&0.1318\\
10& 0.1017&0.1040&0.1063&0.1084&0.1104&0.1123&0.1140&0.1157&0.1172&0.1186\\
11& 0.0749&0.0776&0.0802&0.0828&0.0853&0.0878&0.0902&0.0925&0.0948&0.0970\\
12& 0.0505&0.0530&0.0555&0.0579&0.0604&0.0629&0.0654&0.0679&0.0703&0.0728\\
13& 0.0315&0.0334&0.0354&0.0374&0.0395&0.0416&0.0438&0.0459&0.0481&0.0504\\
14& 0.0182&0.0196&0.0210&0.0225&0.0240&0.0256&0.0272&0.0289&0.0306&0.0324\\
15& 0.0098&0.0107&0.0116&0.0126&0.0136&0.0147&0.0158&0.0169&0.0182&0.0194\\
16& 0.0050&0.0055&0.0060&0.0066&0.0072&0.0079&0.0086&0.0093&0.0101&0.0109\\
17& 0.0024&0.0026&0.0029&0.0033&0.0036&0.0040&0.0044&0.0048&0.0053&0.0058\\
18& 0.0011&0.0012&0.0014&0.0015&0.0017&0.0019&0.0021&0.0024&0.0026&0.0029\\
19& 0.0005&0.0005&0.0006&0.0007&0.0008&0.0009&0.0010&0.0011&0.0012&0.0014\\
20& 0.0002&0.0002&0.0002&0.0003&0.0003&0.0004&0.0004&0.0005&0.0005&0.0006\\
21& 0.0001&0.0001&0.0001&0.0001&0.0001&0.0002&0.0002&0.0002&0.0002&0.0003\\
22& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {9.1}& {9.2}& {9.3}& {9.4}&{9.5}&{9.6}&{9.7}&{9.8}&{9.9}&{10.0}\\\hline
0& 0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&\phantom{0}\\
1& 0.0010&0.0009&0.0009&0.0008&0.0007&0.0007&0.0006&0.0005&0.0005&0.0005\\
2& 0.0046&0.0043&0.0040&0.0037&0.0034&0.0031&0.0029&0.0027&0.0025&0.0023\\
3& 0.0140&0.0131&0.0123&0.0115&0.0107&0.0100&0.0093&0.0087&0.0081&0.0076\\
4& 0.0319&0.0302&0.0285&0.0269&0.0254&0.0240&0.0226&0.0213&0.0201&0.0189\\
5& 0.0581&0.0555&0.0530&0.0506&0.0483&0.0460&0.0439&0.0418&0.0398&0.0378\\
6& 0.0881&0.0851&0.0822&0.0793&0.0764&0.0736&0.0709&0.0682&0.0656&0.0631\\
7& 0.1145&0.1118&0.1091&0.1064&0.1037&0.1010&0.0982&0.0955&0.0928&0.0901\\
8& 0.1302&0.1286&0.1269&0.1251&0.1232&0.1212&0.1191&0.1170&0.1148&0.1126\\
9& 0.1317&0.1315&0.1311&0.1306&0.1300&0.1293&0.1284&0.1274&0.1263&0.1251\\
10& 0.1198&0.1210&0.1219&0.1228&0.1235&0.1241&0.1245&0.1249&0.1250&0.1251\\
11& 0.0991&0.1012&0.1031&0.1049&0.1067&0.1083&0.1098&0.1112&0.1125&0.1137\\
12& 0.0752&0.0776&0.0799&0.0822&0.0844&0.0866&0.0888&0.0908&0.0928&0.0948\\
13& 0.0526&0.0549&0.0572&0.0594&0.0617&0.0640&0.0662&0.0685&0.0707&0.0729\\
14& 0.0342&0.0361&0.0380&0.0399&0.0419&0.0439&0.0459&0.0479&0.0500&0.0521\\
15& 0.0208&0.0221&0.0235&0.0250&0.0265&0.0281&0.0297&0.0313&0.0330&0.0347\\
16& 0.0118&0.0127&0.0137&0.0147&0.0157&0.0168&0.0180&0.0192&0.0204&0.0217\\
17& 0.0063&0.0069&0.0075&0.0081&0.0088&0.0095&0.0103&0.0111&0.0119&0.0128\\
18& 0.0032&0.0035&0.0039&0.0042&0.0046&0.0051&0.0055&0.0060&0.0065&0.0071\\
19& 0.0015&0.0017&0.0019&0.0021&0.0023&0.0026&0.0028&0.0031&0.0034&0.0037\\
20& 0.0007&0.0008&0.0009&0.0010&0.0011&0.0012&0.0014&0.0015&0.0017&0.0019\\
21& 0.0003&0.0003&0.0004&0.0004&0.0005&0.0006&0.0006&0.0007&0.0008&0.0009\\
22& 0.0001&0.0001&0.0002&0.0002&0.0002&0.0002&0.0003&0.0003&0.0004&0.0004\\
23& \phantom{0}&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0001&0.0002&0.0002\\
24& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0001\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {11}& {12}& {13}& {14}&{15}&{16}&{17}&{18}&{19}&{20}\\\hline
0& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
1& 0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
2& 0.0010&0.0004&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
3& 0.0037&0.0018&0.0008&0.0004&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
4& 0.0102&0.0053&0.0027&0.0013&0.0006&0.0003&0.0001&0.0001&\phantom{0}&\phantom{0}\\
5& 0.0224&0.0127&0.0070&0.0037&0.0019&0.0010&0.0005&0.0002&0.0001&0.0001\\
6& 0.0411&0.0255&0.0152&0.0087&0.0048&0.0026&0.0014&0.0007&0.0004&0.0002\\
7& 0.0646&0.0437&0.0281&0.0174&0.0104&0.0060&0.0034&0.0019&0.0010&0.0005\\
8& 0.0888&0.0655&0.0457&0.0304&0.0194&0.0120&0.0072&0.0042&0.0024&0.0013\\
9& 0.1085&0.0874&0.0661&0.0473&0.0324&0.0213&0.0135&0.0083&0.0050&0.0029\\
10& 0.1194&0.1048&0.0859&0.0663&0.0486&0.0341&0.0230&0.0150&0.0095&0.0058\\
11& 0.1194&0.1144&0.1015&0.0844&0.0663&0.0496&0.0355&0.0245&0.0164&0.0106\\
12& 0.1094&0.1144&0.1099&0.0984&0.0829&0.0661&0.0504&0.0368&0.0259&0.0176\\
13& 0.0926&0.1056&0.1099&0.1060&0.0956&0.0814&0.0658&0.0509&0.0378&0.0271\\
14& 0.0728&0.0905&0.1021&0.1060&0.1024&0.0930&0.0800&0.0655&0.0514&0.0387\\
15& 0.0534&0.0724&0.0885&0.0989&0.1024&0.0992&0.0906&0.0786&0.0650&0.0516\\
16& 0.0367&0.0543&0.0719&0.0866&0.0960&0.0992&0.0963&0.0884&0.0772&0.0646\\
17& 0.0237&0.0383&0.0550&0.0713&0.0847&0.0934&0.0963&0.0936&0.0863&0.0760\\
18& 0.0145&0.0255&0.0397&0.0554&0.0706&0.0830&0.0909&0.0936&0.0911&0.0844\\
19& 0.0084&0.0161&0.0272&0.0409&0.0557&0.0699&0.0814&0.0887&0.0911&0.0888\\
20& 0.0046&0.0097&0.0177&0.0286&0.0418&0.0559&0.0692&0.0798&0.0866&0.0888\\
\end{array}
$$
$$
\begin{array}{r|c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}
&&&&&\mu&&&&&\\
x& {11}& {12}& {13}& {14}&{15}&{16}&{17}&{18}&{19}&{20}\\\hline
21& 0.0024&0.0055&0.0109&0.0191&0.0299&0.0426&0.0560&0.0684&0.0783&0.0846\\
22& 0.0012&0.0030&0.0065&0.0121&0.0204&0.0310&0.0433&0.0560&0.0676&0.0769\\
23& 0.0006&0.0016&0.0037&0.0074&0.0133&0.0216&0.0320&0.0438&0.0559&0.0669\\
24& 0.0003&0.0008&0.0020&0.0043&0.0083&0.0144&0.0226&0.0328&0.0442&0.0557\\
25& 0.0001&0.0004&0.0010&0.0024&0.0050&0.0092&0.0154&0.0237&0.0336&0.0446\\
26& \phantom{0}&0.0002&0.0005&0.0013&0.0029&0.0057&0.0101&0.0164&0.0246&0.0343\\
27& \phantom{0}&0.0001&0.0002&0.0007&0.0016&0.0034&0.0063&0.0109&0.0173&0.0254\\
28& \phantom{0}&\phantom{0}&0.0001&0.0003&0.0009&0.0019&0.0038&0.0070&0.0117&0.0181\\
29& \phantom{0}&\phantom{0}&0.0001&0.0002&0.0004&0.0011&0.0023&0.0044&0.0077&0.0125\\
30& \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0006&0.0013&0.0026&0.0049&0.0083\\
31& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0007&0.0015&0.0030&0.0054\\
32& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0004&0.0009&0.0018&0.0034\\
33& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0005&0.0010&0.0020\\
34& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0006&0.0012\\
35& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0007\\
36& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0004\\
37& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002\\
38& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
39& \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
\end{array}
$$
