\documentclass{article} \begin{document} \begin{center} THE POISSONDISTRIBUTION\\ \ \\ Cumulative Distribution Function \end{center} \noindent The columns correspond to different values for the mean ($\lambda$)) 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{center} \begin{tabular}{rr@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r} $x$& \multicolumn{1}{c}{0.1}&\multicolumn{1}{c}{0.2}& \multicolumn{1}{c}{0.3}&\multicolumn{1}{c}{0.4}& \multicolumn{1}{c}{0.5}&\multicolumn{1}{c}{0.6}& \multicolumn{1}{c}{0.7}&\multicolumn{1}{c}{0.8}& \multicolumn{1}{c}{0.9}&\multicolumn{1}{c}{1.0}\\ \ \\ 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\\ \ \\ $x$& \multicolumn{1}{c}{1.1}&\multicolumn{1}{c}{1.2}& \multicolumn{1}{c}{1.3}&\multicolumn{1}{c}{1.4}& \multicolumn{1}{c}{1.5}&\multicolumn{1}{c}{1.6}& \multicolumn{1}{c}{1.7}&\multicolumn{1}{c}{1.8}& \multicolumn{1}{c}{1.9}&\multicolumn{1}{c}{2.0}\\ \ \\ 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\\ \ \\ $x$& \multicolumn{1}{c}{2.2}&\multicolumn{1}{c}{2.4}& \multicolumn{1}{c}{2.6}&\multicolumn{1}{c}{2.8}& \multicolumn{1}{c}{3.0}&\multicolumn{1}{c}{3.2}& \multicolumn{1}{c}{3.4}&\multicolumn{1}{c}{3.6}& \multicolumn{1}{c}{3.8}&\multicolumn{1}{c}{4.0}\\ \ \\ 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{tabular} \end{center} \newpage \begin{center} \begin{tabular}{rr@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r@{\ \,}r} $x$& \multicolumn{1}{c}{4.2}&\multicolumn{1}{c}{4.4}& \multicolumn{1}{c}{4.6}&\multicolumn{1}{c}{4.8}& \multicolumn{1}{c}{5.0}&\multicolumn{1}{c}{5.2}& \multicolumn{1}{c}{5.4}&\multicolumn{1}{c}{5.6}& \multicolumn{1}{c}{5.8}&\multicolumn{1}{c}{6.0}\\ \ \\ 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\\ \ \\ $x$& \multicolumn{1}{c}{6.5}&\multicolumn{1}{c}{7.0}& \multicolumn{1}{c}{7.5}&\multicolumn{1}{c}{8.0}& \multicolumn{1}{c}{8.5}&\multicolumn{1}{c}{9.0}& \multicolumn{1}{c}{9.5}&\multicolumn{1}{c}{10.0}& \multicolumn{1}{c}{10.5}&\multicolumn{1}{c}{11.0}\\ \ \\ 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{tabular} \end{center} \end{document} %
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