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\begin{document}

\noindent\(\pmb{2\text{項分布の場合}}\)

\noindent\(\pmb{\text{PDF}[\text{BinomialDistribution}[8,p],k]}\)

\noindent\((1-p)^{8-k} p^k \text{Binomial}[8,k]\)

\noindent\(\pmb{\text{ListPlot}[\text{Table}[\{k,\text{PDF}[\text{BinomialDistribution}[8,p],k]\},}\\
\pmb{\{p,\{0.3,0.5,0.8\}\},\{k,0,8\}],}\\
\pmb{\text{PlotMarkers} \to  \text{Automatic}, \text{Joined} \to  \text{True},}\\
\pmb{\text{PlotRange} \to  \{0,0.4\}]}\)

\includegraphics{2項とポアソンとベータ-1_gr1.eps}

\noindent\(\pmb{2\text{項係数の値}}\)

\noindent\(\pmb{\text{Table}[\text{Binomial}[8,k],\{k,0,8\}]}\)

\noindent\(\{1,8,28,56,70,56,28,8,1\}\)

\noindent\(\pmb{\text{ポアソン分布の場合}}\)

\noindent\(\pmb{\text{ListPlot}[\text{Table}[\{k,\text{PDF}[\text{PoissonDistribution}[n],k]\},}\\
\pmb{\{n,\{5,13,2\}\},\{k,0,25\}],}\\
\pmb{\text{PlotMarkers} \to  \text{Automatic}, \text{Joined} \to  \text{True},}\\
\pmb{\text{PlotRange} \to  \{0,0.4\}]}\)

\includegraphics{2項とポアソンとベータ-1_gr2.eps}

\noindent\(\pmb{\text{幾何分布の場合}}\)

\noindent\(\pmb{\text{PDF}[\text{GeometricDistribution}[p],k]}\)

\noindent\((1-p)^k p\)

\noindent\(\pmb{\text{ListPlot}[\text{Table}[\{k,\text{PDF}[\text{GeometricDistribution}[p],k]\},}\\
\pmb{\{p,\{0.3,0.5,0.8\}\},\{k,0,10\}],}\\
\pmb{\text{PlotMarkers} \to  \text{Automatic}, \text{Joined} \to  \text{True},}\\
\pmb{\text{PlotRange} \to  \{0,0.8\}]}\)

\includegraphics{2項とポアソンとベータ-1_gr3.eps}

\noindent\(\pmb{\text{PDF}[\text{NormalDistribution}[m,s],x]}\)

\noindent\(\frac{e^{-\frac{(-m+x)^2}{2 s^2}}}{\sqrt{2 \pi } s}\)

\noindent\(\pmb{\text{PDF}[\text{ChiSquareDistribution}[n],x]}\)

\noindent\(\frac{2^{-n/2} e^{-x/2} x^{-1+\frac{n}{2}}}{\text{Gamma}\left[\frac{n}{2}\right]}\)

\noindent\(\pmb{\text{PDF}[\text{BetaDistribution}[a,b],x]}\)

\noindent\(\frac{(1-x)^{-1+b} x^{-1+a}}{\text{Beta}[a,b]}\)

\noindent\(\pmb{\text{Plot}[\{}\\
\pmb{\text{PDF}[\text{BetaDistribution}[0.1,1.0],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[1.0,2.0],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[0.5,1.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[2.0,0.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[3.0,0.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[5.0,0.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[2.0,2.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[3.0,2.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[5.0,2.5],x]\},\{x,0,1\},}\\
\pmb{\text{PlotRange} \to  \{0,5\}]}\)

\includegraphics{2項とポアソンとベータ-1_gr4.eps}

\noindent\(\pmb{\text{ベータ分布その１}（\text{左端で大きくなるとき}）}\)

\noindent\(\pmb{\text{Plot}[\{\text{PDF}[\text{BetaDistribution}[0.1,1.0],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[1.0,2.0],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[0.5,1.5],x],}\\
\pmb{\},\{x,0,1\},}\\
\pmb{\text{PlotRange} \to  \{0,5\}]}\)

\includegraphics{2項とポアソンとベータ-1_gr5.eps}

\noindent\(\pmb{\text{ベータ分布その２}(\text{右端で大きくなるとき})}\)

\noindent\(\pmb{\text{Plot}[\{}\\
\pmb{\text{PDF}[\text{BetaDistribution}[2.0,1.0],x],\text{PDF}[\text{BetaDistribution}[2.0,0.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[3.0,0.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[5.0,0.5],x],}\\
\pmb{\},\{x,0,1\},}\\
\pmb{\text{PlotRange} \to  \{0,5\}]}\\
\pmb{}\)

\includegraphics{2項とポアソンとベータ-1_gr6.eps}

\noindent\(\pmb{\text{ベータ分布その３}(\text{一つ山の形})}\\
\pmb{}\\
\pmb{\text{Plot}[\{\text{PDF}[\text{BetaDistribution}[2.0,2.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[3.0,2.5],x],\text{PDF}[\text{BetaDistribution}[5.0,2.5],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[5.0,5.0],x],}\\
\pmb{\text{PDF}[\text{BetaDistribution}[8.0,8.0],x]\},\{x,0,1\},}\\
\pmb{\text{PlotRange} \to  \{0,4\}]}\)

\noindent\(\text{ベータ分布その３}\)

\includegraphics{2項とポアソンとベータ-1_gr7.eps}

\end{document}
