
\hfuzz=50pt
% Tables:
\newpage
\vspace{2cm}
\begin{tiny}
\begin{center}
\underline{\normalsize 95\% Percentiles of $F$ distribution for various degrees of freedom}
\end{center}
\setlength{\tabcolsep}{0.6mm}
\vspace{-3mm}
\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
$v_1$\textbackslash $v_2$&1&2&3&4&5&6&7&8&9&10&11&12&13&14&15&16&17&18&19&20&21&22&23&24&25\\ \hline
1&161.4&18.51&10.13&7.709&6.608&5.987&5.591&5.318&5.117&4.965&4.844&4.747&4.667&4.600&4.543&4.494&4.451&4.414&4.381&4.351&4.325&4.301&4.279&4.260&4.242\\ \hline
2&199.5&19.00&9.552&6.944&5.786&5.143&4.737&4.459&4.256&4.103&3.982&3.885&3.806&3.739&3.682&3.634&3.592&3.555&3.522&3.493&3.467&3.443&3.422&3.403&3.385\\ \hline
3&215.7&19.16&9.277&6.591&5.409&4.757&4.347&4.066&3.863&3.708&3.587&3.490&3.411&3.344&3.287&3.239&3.197&3.160&3.127&3.098&3.072&3.049&3.028&3.009&2.991\\ \hline
4&224.6&19.25&9.117&6.388&5.192&4.534&4.120&3.838&3.633&3.478&3.357&3.259&3.179&3.112&3.056&3.007&2.965&2.928&2.895&2.866&2.840&2.817&2.796&2.776&2.759\\ \hline
5&230.2&19.30&9.013&6.256&5.050&4.387&3.972&3.687&3.482&3.326&3.204&3.106&3.025&2.958&2.901&2.852&2.810&2.773&2.740&2.711&2.685&2.661&2.640&2.621&2.603\\ \hline
6&234.0&19.33&8.941&6.163&4.950&4.284&3.866&3.581&3.374&3.217&3.095&2.996&2.915&2.848&2.790&2.741&2.699&2.661&2.628&2.599&2.573&2.549&2.528&2.508&2.490\\ \hline
7&236.8&19.35&8.887&6.094&4.876&4.207&3.787&3.500&3.293&3.135&3.012&2.913&2.832&2.764&2.707&2.657&2.614&2.577&2.544&2.514&2.488&2.464&2.442&2.423&2.405\\ \hline
8&238.9&19.37&8.845&6.041&4.818&4.147&3.726&3.438&3.230&3.072&2.948&2.849&2.767&2.699&2.641&2.591&2.548&2.510&2.477&2.447&2.420&2.397&2.375&2.355&2.337\\ \hline
9&240.5&19.38&8.812&5.999&4.772&4.099&3.677&3.388&3.179&3.020&2.896&2.796&2.714&2.646&2.588&2.538&2.494&2.456&2.423&2.393&2.366&2.342&2.320&2.300&2.282\\ \hline
10&241.9&19.40&8.786&5.964&4.735&4.060&3.637&3.347&3.137&2.978&2.854&2.753&2.671&2.602&2.544&2.494&2.450&2.412&2.378&2.348&2.321&2.297&2.275&2.255&2.236\\ \hline
11&243.0&19.40&8.763&5.936&4.704&4.027&3.603&3.313&3.102&2.943&2.818&2.717&2.635&2.565&2.507&2.456&2.413&2.374&2.340&2.310&2.283&2.259&2.236&2.216&2.198\\ \hline
12&243.9&19.41&8.745&5.912&4.678&4.000&3.575&3.284&3.073&2.913&2.788&2.687&2.604&2.534&2.475&2.425&2.381&2.342&2.308&2.278&2.250&2.226&2.204&2.183&2.165\\ \hline
\end{tabular}

\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
$v_1$\textbackslash $v_2$&26&27&28&29&30&31&32&33&34&35&36&37&38&39&40&41&42&43&44&45&46&47&48&49&50\\ \hline
1&4.225&4.210&4.196&4.183&4.171&4.160&4.149&4.139&4.130&4.121&4.113&4.105&4.098&4.091&4.085&4.079&4.073&4.067&4.062&4.057&4.052&4.047&4.043&4.038&4.034\\ \hline
2&3.369&3.354&3.340&3.328&3.316&3.305&3.295&3.285&3.276&3.267&3.259&3.252&3.245&3.238&3.232&3.226&3.220&3.214&3.209&3.204&3.200&3.195&3.191&3.187&3.183\\ \hline
3&2.975&2.960&2.947&2.934&2.922&2.911&2.901&2.892&2.883&2.874&2.866&2.859&2.852&2.845&2.839&2.833&2.827&2.822&2.816&2.812&2.807&2.802&2.798&2.794&2.790\\ \hline
4&2.743&2.728&2.714&2.701&2.690&2.679&2.668&2.659&2.650&2.641&2.634&2.626&2.619&2.612&2.606&2.600&2.594&2.589&2.584&2.579&2.574&2.570&2.565&2.561&2.557\\ \hline
5&2.587&2.572&2.558&2.545&2.534&2.523&2.512&2.503&2.494&2.485&2.477&2.470&2.463&2.456&2.449&2.443&2.438&2.432&2.427&2.422&2.417&2.413&2.409&2.404&2.400\\ \hline
6&2.474&2.459&2.445&2.432&2.421&2.409&2.399&2.389&2.380&2.372&2.364&2.356&2.349&2.342&2.336&2.330&2.324&2.318&2.313&2.308&2.304&2.299&2.295&2.290&2.286\\ \hline
7&2.388&2.373&2.359&2.346&2.334&2.323&2.313&2.303&2.294&2.285&2.277&2.270&2.262&2.255&2.249&2.243&2.237&2.232&2.226&2.221&2.216&2.212&2.207&2.203&2.199\\ \hline
8&2.321&2.305&2.291&2.278&2.266&2.255&2.244&2.235&2.225&2.217&2.209&2.201&2.194&2.187&2.180&2.174&2.168&2.163&2.157&2.152&2.147&2.143&2.138&2.134&2.130\\ \hline
9&2.265&2.250&2.236&2.223&2.211&2.199&2.189&2.179&2.170&2.161&2.153&2.145&2.138&2.131&2.124&2.118&2.112&2.106&2.101&2.096&2.091&2.086&2.082&2.077&2.073\\ \hline
10&2.220&2.204&2.190&2.177&2.165&2.153&2.142&2.133&2.123&2.114&2.106&2.098&2.091&2.084&2.077&2.071&2.065&2.059&2.054&2.049&2.044&2.039&2.035&2.030&2.026\\ \hline
11&2.181&2.166&2.151&2.138&2.126&2.114&2.103&2.093&2.084&2.075&2.067&2.059&2.051&2.044&2.038&2.031&2.025&2.020&2.014&2.009&2.004&1.999&1.995&1.990&1.986\\ \hline
12&2.148&2.132&2.118&2.104&2.092&2.080&2.070&2.060&2.050&2.041&2.033&2.025&2.017&2.010&2.003&1.997&1.991&1.985&1.980&1.974&1.969&1.965&1.960&1.956&1.952\\ \hline
\end{tabular}

\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
$v_1$\textbackslash $v_2$&51&52&53&54&55&56&57&58&59&60&61&62&63&64&65&66&67&68&69&70&71&72&73&74&75\\ \hline
1&4.030&4.027&4.023&4.020&4.016&4.013&4.010&4.007&4.004&4.001&3.998&3.996&3.993&3.991&3.989&3.986&3.984&3.982&3.980&3.978&3.976&3.974&3.972&3.970&3.968\\ \hline
2&3.179&3.175&3.172&3.168&3.165&3.162&3.159&3.156&3.153&3.150&3.148&3.145&3.143&3.140&3.138&3.136&3.134&3.132&3.130&3.128&3.126&3.124&3.122&3.120&3.119\\ \hline
3&2.786&2.783&2.779&2.776&2.773&2.769&2.766&2.764&2.761&2.758&2.755&2.753&2.751&2.748&2.746&2.744&2.742&2.740&2.737&2.736&2.734&2.732&2.730&2.728&2.727\\ \hline
4&2.553&2.550&2.546&2.543&2.540&2.537&2.534&2.531&2.528&2.525&2.523&2.520&2.518&2.515&2.513&2.511&2.509&2.507&2.505&2.503&2.501&2.499&2.497&2.495&2.494\\ \hline
5&2.397&2.393&2.389&2.386&2.383&2.380&2.377&2.374&2.371&2.368&2.366&2.363&2.361&2.358&2.356&2.354&2.352&2.350&2.348&2.346&2.344&2.342&2.340&2.338&2.337\\ \hline
6&2.283&2.279&2.275&2.272&2.269&2.266&2.263&2.260&2.257&2.254&2.251&2.249&2.246&2.244&2.242&2.239&2.237&2.235&2.233&2.231&2.229&2.227&2.226&2.224&2.222\\ \hline
7&2.195&2.192&2.188&2.185&2.181&2.178&2.175&2.172&2.169&2.167&2.164&2.161&2.159&2.156&2.154&2.152&2.150&2.148&2.145&2.143&2.142&2.140&2.138&2.136&2.134\\ \hline
8&2.126&2.122&2.119&2.115&2.112&2.109&2.106&2.103&2.100&2.097&2.094&2.092&2.089&2.087&2.084&2.082&2.080&2.078&2.076&2.074&2.072&2.070&2.068&2.066&2.064\\ \hline
9&2.069&2.066&2.062&2.059&2.055&2.052&2.049&2.046&2.043&2.040&2.037&2.035&2.032&2.030&2.027&2.025&2.023&2.021&2.019&2.017&2.015&2.013&2.011&2.009&2.007\\ \hline
10&2.022&2.018&2.015&2.011&2.008&2.005&2.001&1.998&1.995&1.993&1.990&1.987&1.985&1.982&1.980&1.977&1.975&1.973&1.971&1.969&1.967&1.965&1.963&1.961&1.959\\ \hline
11&1.982&1.978&1.975&1.971&1.968&1.964&1.961&1.958&1.955&1.952&1.949&1.947&1.944&1.942&1.939&1.937&1.935&1.932&1.930&1.928&1.926&1.924&1.922&1.921&1.919\\ \hline
12&1.947&1.944&1.940&1.936&1.933&1.930&1.926&1.923&1.920&1.917&1.915&1.912&1.909&1.907&1.904&1.902&1.900&1.897&1.895&1.893&1.891&1.889&1.887&1.885&1.884\\ \hline
\end{tabular}
\end{tiny}

\begin{center}
\underline{\normalsize Inverse CDF of t distribution for various quantiles}
\end{center}
\vspace{-1mm}
\setlength{\tabcolsep}{0.8mm}
\begin{tiny}
\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|l|c|c|c|c|c|c|c|c|l|c|c|c|c|c|c|c|c|} \hline
\textbf{v\textbackslash q}&\textbf{0.995}&\textbf{0.99}&\textbf{0.98}&\textbf{0.975}&\textbf{0.95}&\textbf{0.9}&\textbf{0.8}&\textbf{}&\textbf{v\textbackslash q}&\textbf{0.995}&\textbf{0.99}&\textbf{0.98}&\textbf{0.975}&\textbf{0.95}&\textbf{0.9}&\textbf{0.8}&\textbf{}&\textbf{v\textbackslash q}&\textbf{0.995}&\textbf{0.99}&\textbf{0.98}&\textbf{0.975}&\textbf{0.95}&\textbf{0.9}&\textbf{0.8}\\ \hline
\textbf{1}&63.66&31.82&15.89&12.71&6.314&3.078&1.376&&\textbf{31}&2.744&2.453&2.144&2.040&1.696&1.309&0.853&&\textbf{61}&2.659&2.389&2.099&2.000&1.670&1.296&0.848\\ \hline
\textbf{2}&9.925&6.965&4.849&4.303&2.920&1.886&1.061&&\textbf{32}&2.738&2.449&2.141&2.037&1.694&1.309&0.853&&\textbf{62}&2.657&2.388&2.098&1.999&1.670&1.295&0.847\\ \hline
\textbf{3}&5.841&4.541&3.482&3.182&2.353&1.638&0.978&&\textbf{33}&2.733&2.445&2.138&2.035&1.692&1.308&0.853&&\textbf{63}&2.656&2.387&2.097&1.998&1.669&1.295&0.847\\ \hline
\textbf{4}&4.604&3.747&2.999&2.776&2.132&1.533&0.941&&\textbf{34}&2.728&2.441&2.136&2.032&1.691&1.307&0.852&&\textbf{64}&2.655&2.386&2.096&1.998&1.669&1.295&0.847\\ \hline
\textbf{5}&4.032&3.365&2.757&2.571&2.015&1.476&0.920&&\textbf{35}&2.724&2.438&2.133&2.030&1.690&1.306&0.852&&\textbf{65}&2.654&2.385&2.096&1.997&1.669&1.295&0.847\\ \hline
\textbf{6}&3.707&3.143&2.612&2.447&1.943&1.440&0.906&&\textbf{36}&2.719&2.434&2.131&2.028&1.688&1.306&0.852&&\textbf{66}&2.652&2.384&2.095&1.997&1.668&1.295&0.847\\ \hline
\textbf{7}&3.499&2.998&2.517&2.365&1.895&1.415&0.896&&\textbf{37}&2.715&2.431&2.129&2.026&1.687&1.305&0.851&&\textbf{67}&2.651&2.383&2.095&1.996&1.668&1.294&0.847\\ \hline
\textbf{8}&3.355&2.896&2.449&2.306&1.860&1.397&0.889&&\textbf{38}&2.712&2.429&2.127&2.024&1.686&1.304&0.851&&\textbf{68}&2.650&2.382&2.094&1.995&1.668&1.294&0.847\\ \hline
\textbf{9}&3.250&2.821&2.398&2.262&1.833&1.383&0.883&&\textbf{39}&2.708&2.426&2.125&2.023&1.685&1.304&0.851&&\textbf{69}&2.649&2.382&2.093&1.995&1.667&1.294&0.847\\ \hline
\textbf{10}&3.169&2.764&2.359&2.228&1.812&1.372&0.879&&\textbf{40}&2.704&2.423&2.123&2.021&1.684&1.303&0.851&&\textbf{70}&2.648&2.381&2.093&1.994&1.667&1.294&0.847\\ \hline
\textbf{11}&3.106&2.718&2.328&2.201&1.796&1.363&0.876&&\textbf{41}&2.701&2.421&2.121&2.020&1.683&1.303&0.850&&\textbf{71}&2.647&2.380&2.092&1.994&1.667&1.294&0.847\\ \hline
\textbf{12}&3.055&2.681&2.303&2.179&1.782&1.356&0.873&&\textbf{42}&2.698&2.418&2.120&2.018&1.682&1.302&0.850&&\textbf{72}&2.646&2.379&2.092&1.993&1.666&1.293&0.847\\ \hline
\textbf{13}&3.012&2.650&2.282&2.160&1.771&1.350&0.870&&\textbf{43}&2.695&2.416&2.118&2.017&1.681&1.302&0.850&&\textbf{73}&2.645&2.379&2.091&1.993&1.666&1.293&0.847\\ \hline
\textbf{14}&2.977&2.624&2.264&2.145&1.761&1.345&0.868&&\textbf{44}&2.692&2.414&2.116&2.015&1.680&1.301&0.850&&\textbf{74}&2.644&2.378&2.091&1.993&1.666&1.293&0.847\\ \hline
\textbf{15}&2.947&2.602&2.249&2.131&1.753&1.341&0.866&&\textbf{45}&2.690&2.412&2.115&2.014&1.679&1.301&0.850&&\textbf{75}&2.643&2.377&2.090&1.992&1.665&1.293&0.846\\ \hline
\textbf{16}&2.921&2.583&2.235&2.120&1.746&1.337&0.865&&\textbf{46}&2.687&2.410&2.114&2.013&1.679&1.300&0.850&&\textbf{76}&2.642&2.376&2.090&1.992&1.665&1.293&0.846\\ \hline
\textbf{17}&2.898&2.567&2.224&2.110&1.740&1.333&0.863&&\textbf{47}&2.685&2.408&2.112&2.012&1.678&1.300&0.849&&\textbf{77}&2.641&2.376&2.089&1.991&1.665&1.293&0.846\\ \hline
\textbf{18}&2.878&2.552&2.214&2.101&1.734&1.330&0.862&&\textbf{48}&2.682&2.407&2.111&2.011&1.677&1.299&0.849&&\textbf{78}&2.640&2.375&2.089&1.991&1.665&1.292&0.846\\ \hline
\textbf{19}&2.861&2.539&2.205&2.093&1.729&1.328&0.861&&\textbf{49}&2.680&2.405&2.110&2.010&1.677&1.299&0.849&&\textbf{79}&2.640&2.374&2.088&1.990&1.664&1.292&0.846\\ \hline
\textbf{20}&2.845&2.528&2.197&2.086&1.725&1.325&0.860&&\textbf{50}&2.678&2.403&2.109&2.009&1.676&1.299&0.849&&\textbf{80}&2.639&2.374&2.088&1.990&1.664&1.292&0.846\\ \hline
\textbf{21}&2.831&2.518&2.189&2.080&1.721&1.323&0.859&&\textbf{51}&2.676&2.402&2.108&2.008&1.675&1.298&0.849&&\textbf{81}&2.638&2.373&2.087&1.990&1.664&1.292&0.846\\ \hline
\textbf{22}&2.819&2.508&2.183&2.074&1.717&1.321&0.858&&\textbf{52}&2.674&2.400&2.107&2.007&1.675&1.298&0.849&&\textbf{82}&2.637&2.373&2.087&1.989&1.664&1.292&0.846\\ \hline
\textbf{23}&2.807&2.500&2.177&2.069&1.714&1.319&0.858&&\textbf{53}&2.672&2.399&2.106&2.006&1.674&1.298&0.848&&\textbf{83}&2.636&2.372&2.087&1.989&1.663&1.292&0.846\\ \hline
\textbf{24}&2.797&2.492&2.172&2.064&1.711&1.318&0.857&&\textbf{54}&2.670&2.397&2.105&2.005&1.674&1.297&0.848&&\textbf{84}&2.636&2.372&2.086&1.989&1.663&1.292&0.846\\ \hline
\textbf{25}&2.787&2.485&2.167&2.060&1.708&1.316&0.856&&\textbf{55}&2.668&2.396&2.104&2.004&1.673&1.297&0.848&&\textbf{85}&2.635&2.371&2.086&1.988&1.663&1.292&0.846\\ \hline
\textbf{26}&2.779&2.479&2.162&2.056&1.706&1.315&0.856&&\textbf{56}&2.667&2.395&2.103&2.003&1.673&1.297&0.848&&\textbf{86}&2.634&2.370&2.085&1.988&1.663&1.291&0.846\\ \hline
\textbf{27}&2.771&2.473&2.158&2.052&1.703&1.314&0.855&&\textbf{57}&2.665&2.394&2.102&2.002&1.672&1.297&0.848&&\textbf{87}&2.634&2.370&2.085&1.988&1.663&1.291&0.846\\ \hline
\textbf{28}&2.763&2.467&2.154&2.048&1.701&1.313&0.855&&\textbf{58}&2.663&2.392&2.101&2.002&1.672&1.296&0.848&&\textbf{88}&2.633&2.369&2.085&1.987&1.662&1.291&0.846\\ \hline
\textbf{29}&2.756&2.462&2.150&2.045&1.699&1.311&0.854&&\textbf{59}&2.662&2.391&2.100&2.001&1.671&1.296&0.848&&\textbf{89}&2.632&2.369&2.084&1.987&1.662&1.291&0.846\\ \hline
\textbf{30}&2.750&2.457&2.147&2.042&1.697&1.310&0.854&&\textbf{60}&2.660&2.390&2.099&2.000&1.671&1.296&0.848&&\textbf{90}&2.632&2.368&2.084&1.987&1.662&1.291&0.846\\ \hline
\end{tabular}


\newpage
\vspace*{-2cm}
\begin{center}
\underline{\normalsize CDF values of standard Normal distribution}
\end{center}
\vspace{-4mm}
\setlength{\tabcolsep}{1.6mm}
\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
x&$\Phi(x)$&&x&$\Phi(x)$&&x&$\Phi(x)$&&x&$\Phi(x)$&&x&$\Phi(x)$&&x&$\Phi(x)$&&x&$\Phi(x)$&&x&$\Phi(x)$&&x&$\Phi(x)$\\ \hline
0.01&0.5040&&0.41&0.6591&&0.81&0.7910&&1.21&0.8869&&1.61&0.9463&&2.01&0.9778&&2.41&0.9920&&2.81&0.9975&&3.21&0.9993\\ \hline
0.02&0.5080&&0.42&0.6628&&0.82&0.7939&&1.22&0.8888&&1.62&0.9474&&2.02&0.9783&&2.42&0.9922&&2.82&0.9976&&3.22&0.9994\\ \hline
0.03&0.5120&&0.43&0.6664&&0.83&0.7967&&1.23&0.8907&&1.63&0.9484&&2.03&0.9788&&2.43&0.9925&&2.83&0.9977&&3.23&0.9994\\ \hline
0.04&0.5160&&0.44&0.6700&&0.84&0.7995&&1.24&0.8925&&1.64&0.9495&&2.04&0.9793&&2.44&0.9927&&2.84&0.9977&&3.24&0.9994\\ \hline
0.05&0.5199&&0.45&0.6736&&0.85&0.8023&&1.25&0.8944&&1.65&0.9505&&2.05&0.9798&&2.45&0.9929&&2.85&0.9978&&3.25&0.9994\\ \hline
0.06&0.5239&&0.46&0.6772&&0.86&0.8051&&1.26&0.8962&&1.66&0.9515&&2.06&0.9803&&2.46&0.9931&&2.86&0.9979&&3.26&0.9994\\ \hline
0.07&0.5279&&0.47&0.6808&&0.87&0.8078&&1.27&0.8980&&1.67&0.9525&&2.07&0.9808&&2.47&0.9932&&2.87&0.9979&&3.27&0.9995\\ \hline
0.08&0.5319&&0.48&0.6844&&0.88&0.8106&&1.28&0.8997&&1.68&0.9535&&2.08&0.9812&&2.48&0.9934&&2.88&0.9980&&3.28&0.9995\\ \hline
0.09&0.5359&&0.49&0.6879&&0.89&0.8133&&1.29&0.9015&&1.69&0.9545&&2.09&0.9817&&2.49&0.9936&&2.89&0.9981&&3.29&0.9995\\ \hline
0.1&0.5398&&0.5&0.6915&&0.9&0.8159&&1.3&0.9032&&1.7&0.9554&&2.1&0.9821&&2.5&0.9938&&2.9&0.9981&&3.3&0.9995\\ \hline
0.11&0.5438&&0.51&0.6950&&0.91&0.8186&&1.31&0.9049&&1.71&0.9564&&2.11&0.9826&&2.51&0.9940&&2.91&0.9982&&3.31&0.9995\\ \hline
0.12&0.5478&&0.52&0.6985&&0.92&0.8212&&1.32&0.9066&&1.72&0.9573&&2.12&0.9830&&2.52&0.9941&&2.92&0.9982&&3.32&0.9995\\ \hline
0.13&0.5517&&0.53&0.7019&&0.93&0.8238&&1.33&0.9082&&1.73&0.9582&&2.13&0.9834&&2.53&0.9943&&2.93&0.9983&&3.33&0.9996\\ \hline
0.14&0.5557&&0.54&0.7054&&0.94&0.8264&&1.34&0.9099&&1.74&0.9591&&2.14&0.9838&&2.54&0.9945&&2.94&0.9984&&3.34&0.9996\\ \hline
0.15&0.5596&&0.55&0.7088&&0.95&0.8289&&1.35&0.9115&&1.75&0.9599&&2.15&0.9842&&2.55&0.9946&&2.95&0.9984&&3.35&0.9996\\ \hline
0.16&0.5636&&0.56&0.7123&&0.96&0.8315&&1.36&0.9131&&1.76&0.9608&&2.16&0.9846&&2.56&0.9948&&2.96&0.9985&&3.36&0.9996\\ \hline
0.17&0.5675&&0.57&0.7157&&0.97&0.8340&&1.37&0.9147&&1.77&0.9616&&2.17&0.9850&&2.57&0.9949&&2.97&0.9985&&3.37&0.9996\\ \hline
0.18&0.5714&&0.58&0.7190&&0.98&0.8365&&1.38&0.9162&&1.78&0.9625&&2.18&0.9854&&2.58&0.9951&&2.98&0.9986&&3.38&0.9996\\ \hline
0.19&0.5753&&0.59&0.7224&&0.99&0.8389&&1.39&0.9177&&1.79&0.9633&&2.19&0.9857&&2.59&0.9952&&2.99&0.9986&&3.39&0.9997\\ \hline
0.2&0.5793&&0.6&0.7257&&1&0.8413&&1.4&0.9192&&1.8&0.9641&&2.2&0.9861&&2.6&0.9953&&3&0.9987&&3.4&0.9997\\ \hline
0.21&0.5832&&0.61&0.7291&&1.01&0.8438&&1.41&0.9207&&1.81&0.9649&&2.21&0.9864&&2.61&0.9955&&3.01&0.9987&&3.41&0.9997\\ \hline
0.22&0.5871&&0.62&0.7324&&1.02&0.8461&&1.42&0.9222&&1.82&0.9656&&2.22&0.9868&&2.62&0.9956&&3.02&0.9987&&3.42&0.9997\\ \hline
0.23&0.5910&&0.63&0.7357&&1.03&0.8485&&1.43&0.9236&&1.83&0.9664&&2.23&0.9871&&2.63&0.9957&&3.03&0.9988&&3.43&0.9997\\ \hline
0.24&0.5948&&0.64&0.7389&&1.04&0.8508&&1.44&0.9251&&1.84&0.9671&&2.24&0.9875&&2.64&0.9959&&3.04&0.9988&&3.44&0.9997\\ \hline
0.25&0.5987&&0.65&0.7422&&1.05&0.8531&&1.45&0.9265&&1.85&0.9678&&2.25&0.9878&&2.65&0.9960&&3.05&0.9989&&3.45&0.9997\\ \hline
0.26&0.6026&&0.66&0.7454&&1.06&0.8554&&1.46&0.9279&&1.86&0.9686&&2.26&0.9881&&2.66&0.9961&&3.06&0.9989&&3.46&0.9997\\ \hline
0.27&0.6064&&0.67&0.7486&&1.07&0.8577&&1.47&0.9292&&1.87&0.9693&&2.27&0.9884&&2.67&0.9962&&3.07&0.9989&&3.47&0.9997\\ \hline
0.28&0.6103&&0.68&0.7517&&1.08&0.8599&&1.48&0.9306&&1.88&0.9699&&2.28&0.9887&&2.68&0.9963&&3.08&0.9990&&3.48&0.9997\\ \hline
0.29&0.6141&&0.69&0.7549&&1.09&0.8621&&1.49&0.9319&&1.89&0.9706&&2.29&0.9890&&2.69&0.9964&&3.09&0.9990&&3.49&0.9998\\ \hline
0.3&0.6179&&0.7&0.7580&&1.1&0.8643&&1.5&0.9332&&1.9&0.9713&&2.3&0.9893&&2.7&0.9965&&3.1&0.9990&&3.5&0.9998\\ \hline
0.31&0.6217&&0.71&0.7611&&1.11&0.8665&&1.51&0.9345&&1.91&0.9719&&2.31&0.9896&&2.71&0.9966&&3.11&0.9991&&3.51&0.9998\\ \hline
0.32&0.6255&&0.72&0.7642&&1.12&0.8686&&1.52&0.9357&&1.92&0.9726&&2.32&0.9898&&2.72&0.9967&&3.12&0.9991&&3.52&0.9998\\ \hline
0.33&0.6293&&0.73&0.7673&&1.13&0.8708&&1.53&0.9370&&1.93&0.9732&&2.33&0.9901&&2.73&0.9968&&3.13&0.9991&&3.53&0.9998\\ \hline
0.34&0.6331&&0.74&0.7704&&1.14&0.8729&&1.54&0.9382&&1.94&0.9738&&2.34&0.9904&&2.74&0.9969&&3.14&0.9992&&3.54&0.9998\\ \hline
0.35&0.6368&&0.75&0.7734&&1.15&0.8749&&1.55&0.9394&&1.95&0.9744&&2.35&0.9906&&2.75&0.9970&&3.15&0.9992&&3.55&0.9998\\ \hline
0.36&0.6406&&0.76&0.7764&&1.16&0.8770&&1.56&0.9406&&1.96&0.9750&&2.36&0.9909&&2.76&0.9971&&3.16&0.9992&&3.56&0.9998\\ \hline
0.37&0.6443&&0.77&0.7794&&1.17&0.8790&&1.57&0.9418&&1.97&0.9756&&2.37&0.9911&&2.77&0.9972&&3.17&0.9992&&3.57&0.9998\\ \hline
0.38&0.6480&&0.78&0.7823&&1.18&0.8810&&1.58&0.9429&&1.98&0.9761&&2.38&0.9913&&2.78&0.9973&&3.18&0.9993&&3.58&0.9998\\ \hline
0.39&0.6517&&0.79&0.7852&&1.19&0.8830&&1.59&0.9441&&1.99&0.9767&&2.39&0.9916&&2.79&0.9974&&3.19&0.9993&&3.59&0.9998\\ \hline
0.4&0.6554&&0.8&0.7881&&1.2&0.8849&&1.6&0.9452&&2&0.9772&&2.4&0.9918&&2.8&0.9974&&3.2&0.9993&&3.6&0.9998\\ \hline
\end{tabular}

\begin{center}
\underline{\normalsize CDF values of $\chi^2$ distribution}
\end{center}
\setlength{\tabcolsep}{0.6mm}
\vspace{-3mm}
\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
\textbf{v}\textbackslash\textbf{x}&\textbf{0.3}&\textbf{0.6}&\textbf{0.9}&\textbf{1.2}&\textbf{1.5}&\textbf{1.8}&\textbf{2.1}&\textbf{2.4}&\textbf{2.7}&\textbf{3}&\textbf{3.3}&\textbf{3.6}&\textbf{3.9}&\textbf{4.2}&\textbf{4.5}&\textbf{4.8}&\textbf{5.1}&\textbf{5.4}&\textbf{5.7}&\textbf{6}&\textbf{6.3}&\textbf{6.6}&\textbf{6.9}&\textbf{7.2}&\textbf{7.5}&\textbf{7.8}\\ \hline
\textbf{1}&0.416&0.561&0.657&0.727&0.779&0.820&0.853&0.879&0.900&0.917&0.931&0.942&0.952&0.960&0.966&0.972&0.976&0.980&0.983&0.986&0.988&0.990&0.991&0.993&0.994 &0.995\\ \hline
\textbf{2}&0.139&0.259&0.362&0.451&0.528&0.593&0.650&0.699&0.741&0.777&0.808&0.835&0.858&0.878&0.895&0.909&0.922&0.933&0.942&0.950&0.957&0.963&0.968&0.973&0.976 &0.980\\ \hline
\textbf{3}&0.040&0.104&0.175&0.247&0.318&0.385&0.448&0.506&0.560&0.608&0.652&0.692&0.728&0.759&0.788&0.813&0.835&0.855&0.873&0.888&0.902&0.914&0.925&0.934&0.942 &0.950\\ \hline
\textbf{4}&0.010&0.037&0.075&0.122&0.173&0.228&0.283&0.337&0.391&0.442&0.491&0.537&0.580&0.620&0.657&0.692&0.723&0.751&0.777&0.801&0.822&0.841&0.859&0.874&0.888 &0.901\\ \hline
\textbf{5}&0.002&0.012&0.030&0.055&0.087&0.124&0.165&0.209&0.254&0.300&0.346&0.392&0.436&0.479&0.520&0.559&0.596&0.631&0.663&0.694&0.722&0.748&0.772&0.794&0.814 &0.832\\ \hline
\textbf{6}&0.001&0.004&0.011&0.023&0.041&0.063&0.090&0.121&0.155&0.191&0.230&0.269&0.310&0.350&0.391&0.430&0.469&0.506&0.542&0.577&0.610&0.641&0.670&0.697&0.723 &0.747\\ \hline
\textbf{7}&0.000&0.001&0.004&0.009&0.018&0.030&0.046&0.066&0.089&0.115&0.144&0.175&0.209&0.244&0.279&0.316&0.352&0.389&0.425&0.460&0.495&0.528&0.561&0.592&0.621 &0.649\\ \hline
\textbf{8}&0.000&0.000&0.001&0.003&0.007&0.013&0.022&0.034&0.048&0.066&0.086&0.109&0.134&0.161&0.191&0.221&0.253&0.286&0.319&0.353&0.386&0.420&0.453&0.485&0.516 &0.547\\ \hline
\textbf{9}&0.000&0.000&0.000&0.001&0.003&0.006&0.010&0.017&0.025&0.036&0.049&0.064&0.082&0.102&0.124&0.149&0.174&0.202&0.230&0.260&0.290&0.321&0.352&0.384&0.415 &0.446\\ \hline
\textbf{10}&0.000&0.000&0.000&0.000&0.001&0.002&0.004&0.008&0.012&0.019&0.027&0.036&0.048&0.062&0.078&0.096&0.116&0.137&0.160&0.185&0.211&0.237&0.265&0.294&0.322 &0.352\\ \hline
\textbf{11}&0.000&0.000&0.000&0.000&0.000&0.001&0.002&0.003&0.006&0.009&0.014&0.020&0.027&0.036&0.047&0.060&0.074&0.090&0.107&0.127&0.147&0.170&0.193&0.217&0.243 &0.269\\ \hline
\textbf{12}&0.000&0.000&0.000&0.000&0.000&0.000&0.001&0.002&0.003&0.004&0.007&0.010&0.015&0.020&0.027&0.036&0.045&0.057&0.070&0.084&0.100&0.117&0.136&0.156&0.177 &0.199\\ \hline
\textbf{13}&0.000&0.000&0.000&0.000&0.000&0.000&0.000&0.001&0.001&0.002&0.003&0.005&0.008&0.011&0.015&0.021&0.027&0.035&0.044&0.054&0.065&0.078&0.093&0.108&0.125 &0.144\\ \hline
\textbf{14}&0.000&0.000&0.000&0.000&0.000&0.000&0.000&0.000&0.001&0.001&0.002&0.003&0.004&0.006&0.008&0.012&0.016&0.021&0.027&0.034&0.042&0.051&0.062&0.073&0.086 &0.101\\ \hline
\textbf{15}&0.000&0.000&0.000&0.000&0.000&0.000&0.000&0.000&0.000&0.000&0.001&0.001&0.002&0.003&0.004&0.006&0.009&0.012&0.016&0.020&0.026&0.032&0.040&0.048&0.058 &0.068\\ \hline
\end{tabular}

\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
\textbf{v}\textbackslash\textbf{x}&\textbf{8.1}&\textbf{8.4}&\textbf{8.7}&\textbf{9}&\textbf{9.3}&\textbf{9.6}&\textbf{9.9}&\textbf{10.2}&\textbf{10.5}&\textbf{10.8}&\textbf{11.1}&\textbf{11.4}&\textbf{11.7}&\textbf{12}&\textbf{12.3}&\textbf{12.6}&\textbf{12.9}&\textbf{13.2}&\textbf{13.5}&\textbf{13.8}&\textbf{14.1}&\textbf{14.4}&\textbf{14.7}&\textbf{15}&\textbf{15.3}&\textbf{15.6}\\ \hline
\textbf{1}&0.996&0.996&0.997&0.997&0.998&0.998&0.998&0.999&0.999&0.999&0.999&0.999&0.999&0.999&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000 &1.000\\ \hline
\textbf{2}&0.983&0.985&0.987&0.989&0.990&0.992&0.993&0.994&0.995&0.995&0.996&0.997&0.997&0.998&0.998&0.998&0.998&0.999&0.999&0.999&0.999&0.999&0.999&0.999&1.000 &1.000\\ \hline
\textbf{3}&0.956&0.962&0.966&0.971&0.974&0.978&0.981&0.983&0.985&0.987&0.989&0.990&0.992&0.993&0.994&0.994&0.995&0.996&0.996&0.997&0.997&0.998&0.998&0.998&0.998 &0.999\\ \hline
\textbf{4}&0.912&0.922&0.931&0.939&0.946&0.952&0.958&0.963&0.967&0.971&0.975&0.978&0.980&0.983&0.985&0.987&0.988&0.990&0.991&0.992&0.993&0.994&0.995&0.995&0.996 &0.996\\ \hline
\textbf{5}&0.849&0.864&0.878&0.891&0.902&0.913&0.922&0.930&0.938&0.945&0.951&0.956&0.961&0.965&0.969&0.973&0.976&0.978&0.981&0.983&0.985&0.987&0.988&0.990&0.991 &0.992\\ \hline
\textbf{6}&0.769&0.790&0.809&0.826&0.843&0.857&0.871&0.884&0.895&0.905&0.915&0.923&0.931&0.938&0.944&0.950&0.955&0.960&0.964&0.968&0.971&0.975&0.977&0.980&0.982 &0.984\\ \hline
\textbf{7}&0.676&0.701&0.725&0.747&0.768&0.788&0.806&0.822&0.838&0.852&0.866&0.878&0.889&0.899&0.909&0.918&0.925&0.933&0.939&0.945&0.951&0.955&0.960&0.964&0.968 &0.971\\ \hline
\textbf{8}&0.576&0.605&0.632&0.658&0.682&0.706&0.728&0.749&0.768&0.787&0.804&0.820&0.835&0.849&0.862&0.874&0.885&0.895&0.904&0.913&0.921&0.928&0.935&0.941&0.946 &0.952\\ \hline
\textbf{9}&0.476&0.506&0.535&0.563&0.590&0.616&0.641&0.665&0.688&0.710&0.731&0.751&0.769&0.787&0.803&0.818&0.833&0.846&0.859&0.870&0.881&0.891&0.900&0.909&0.917 &0.924\\ \hline
\textbf{10}&0.381&0.410&0.439&0.468&0.496&0.524&0.551&0.577&0.602&0.627&0.650&0.673&0.694&0.715&0.735&0.753&0.771&0.787&0.803&0.818&0.832&0.844&0.857&0.868&0.878 &0.888\\ \hline
\textbf{11}&0.296&0.323&0.350&0.378&0.406&0.433&0.461&0.488&0.514&0.540&0.565&0.590&0.613&0.636&0.658&0.680&0.700&0.720&0.738&0.756&0.772&0.788&0.803&0.818&0.831 &0.843\\ \hline
\textbf{12}&0.223&0.247&0.272&0.297&0.323&0.349&0.375&0.402&0.428&0.454&0.480&0.505&0.530&0.554&0.578&0.601&0.624&0.645&0.666&0.686&0.706&0.724&0.742&0.759&0.775 &0.790\\ \hline
\textbf{13}&0.163&0.183&0.205&0.227&0.250&0.274&0.298&0.322&0.347&0.372&0.398&0.423&0.448&0.472&0.497&0.521&0.544&0.568&0.590&0.612&0.633&0.654&0.674&0.693&0.711 &0.729\\ \hline
\textbf{14}&0.116&0.133&0.150&0.169&0.189&0.209&0.231&0.253&0.275&0.298&0.322&0.346&0.370&0.394&0.418&0.442&0.466&0.489&0.512&0.535&0.558&0.580&0.601&0.622&0.642 &0.662\\ \hline
\textbf{15}&0.080&0.093&0.107&0.122&0.139&0.156&0.174&0.193&0.213&0.233&0.255&0.276&0.298&0.321&0.344&0.367&0.390&0.413&0.436&0.459&0.482&0.505&0.527&0.549&0.570 &0.591\\ \hline
\end{tabular}

\hspace{-16mm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
\textbf{v}\textbackslash\textbf{x}&\textbf{15.9}&\textbf{16.2}&\textbf{16.5}&\textbf{16.8}&\textbf{17.1}&\textbf{17.4}&\textbf{17.7}&\textbf{18}&\textbf{18.3}&\textbf{18.6}&\textbf{18.9}&\textbf{19.2}&\textbf{19.5}&\textbf{19.8}&\textbf{20.1}&\textbf{20.4}&\textbf{20.7}&\textbf{21}&\textbf{21.3}&\textbf{21.6}&\textbf{21.9}&\textbf{22.2}&\textbf{22.5}&\textbf{22.8}&\textbf{23.1}&\textbf{23.4}\\ \hline
\textbf{1}&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000 &1.000\\ \hline
\textbf{2}&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000 &1.000\\ \hline
\textbf{3}&0.999&0.999&0.999&0.999&0.999&0.999&0.999&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000 &1.000\\ \hline
\textbf{4}&0.997&0.997&0.998&0.998&0.998&0.998&0.999&0.999&0.999&0.999&0.999&0.999&0.999&0.999&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000&1.000 &1.000\\ \hline
\textbf{5}&0.993&0.994&0.994&0.995&0.996&0.996&0.997&0.997&0.997&0.998&0.998&0.998&0.998&0.999&0.999&0.999&0.999&0.999&0.999&0.999&0.999&1.000&1.000&1.000&1.000 &1.000\\ \hline
\textbf{6}&0.986&0.987&0.989&0.990&0.991&0.992&0.993&0.994&0.994&0.995&0.996&0.996&0.997&0.997&0.997&0.998&0.998&0.998&0.998&0.999&0.999&0.999&0.999&0.999&0.999 &0.999\\ \hline
\textbf{7}&0.974&0.977&0.979&0.981&0.983&0.985&0.987&0.988&0.989&0.990&0.991&0.992&0.993&0.994&0.995&0.995&0.996&0.996&0.997&0.997&0.997&0.998&0.998&0.998&0.998 &0.999\\ \hline
\textbf{8}&0.956&0.960&0.964&0.968&0.971&0.974&0.976&0.979&0.981&0.983&0.985&0.986&0.988&0.989&0.990&0.991&0.992&0.993&0.994&0.994&0.995&0.995&0.996&0.996&0.997 &0.997\\ \hline
\textbf{9}&0.931&0.937&0.943&0.948&0.953&0.957&0.961&0.965&0.968&0.971&0.974&0.976&0.979&0.981&0.983&0.984&0.986&0.987&0.989&0.990&0.991&0.992&0.993&0.993&0.994 &0.995\\ \hline
\textbf{10}&0.897&0.906&0.914&0.921&0.928&0.934&0.940&0.945&0.950&0.954&0.958&0.962&0.966&0.969&0.972&0.974&0.977&0.979&0.981&0.983&0.984&0.986&0.987&0.988&0.990 &0.991\\ \hline
\textbf{11}&0.855&0.866&0.876&0.886&0.895&0.903&0.911&0.918&0.925&0.931&0.937&0.942&0.947&0.952&0.956&0.960&0.963&0.967&0.970&0.972&0.975&0.977&0.979&0.981&0.983 &0.984\\ \hline
\textbf{12}&0.804&0.818&0.831&0.843&0.854&0.865&0.875&0.884&0.893&0.901&0.909&0.916&0.923&0.929&0.935&0.940&0.945&0.950&0.954&0.958&0.961&0.965&0.968&0.971&0.973 &0.975\\ \hline
\textbf{13}&0.745&0.762&0.777&0.791&0.805&0.818&0.831&0.842&0.854&0.864&0.874&0.883&0.892&0.900&0.907&0.914&0.921&0.927&0.933&0.938&0.943&0.948&0.952&0.956&0.960 &0.963\\ \hline
\textbf{14}&0.680&0.699&0.716&0.733&0.749&0.765&0.779&0.793&0.807&0.819&0.831&0.843&0.853&0.863&0.873&0.882&0.890&0.898&0.906&0.913&0.919&0.925&0.931&0.936&0.941 &0.946\\ \hline
\textbf{15}&0.611&0.631&0.650&0.669&0.687&0.704&0.721&0.737&0.753&0.768&0.782&0.795&0.808&0.820&0.832&0.843&0.853&0.863&0.872&0.881&0.890&0.897&0.905&0.912&0.918 &0.924\\ \hline
\end{tabular}
\end{tiny}
\vspace*{-2cm}
