<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%This command provides the text to be written
%in the second part of the column 4 on the page 3
%
%The command has one parameter
%        1) The width of the text
\newcommand\TThreeProbTwo[1]{%
   \parbox[t]{#1}{%
      \DisplaySpace{\TThreeDisplaySpace}{\TThreeDisplayShortSpace}
      %Formula 7
      \TThreeTitle{Binomial distribution:}
      \ifluatex
          \AdjustSpace{0ex plus .5ex minus .5ex}
      \else
          \AdjustSpace{1ex plus .5ex minus .5ex}
      \fi
      \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus 1ex}{\BigChar}{\StyleWithoutNumber}
           \def\FirstPart{\Pr[X = k] = \mbox{}}
           \FmPartA{\FirstPart \binom{n}{k} p^k q^{n-k}}
           \FmPartB{\FirstPart}{\MathRemark[\relax]{q = 1-p}},
           \Fm{\E[X] = \sum^n_{k=1} k {n \choose k} p^k q^{n-k} = n p} 
      \end{DisplayFormulae}

      %Formula 8
      \TThreeTitle{Poisson distribution:}%
      \AdjustSpace{.75ex plus .5ex minus .5ex}
      \raggedright
       \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus 1ex}{\SmallChar}{\StyleWithoutNumber}
          \Fm{\Pr[X = k] = \frac{e^{-\lambda} \lambda^k}{k!}}, 
          \Fm{\E[X] = \lambda}
       \end{DisplayFormulae}

       %To push a little bit the text to the top and
       %separate it from the bottom of the NiceTabular environment.
       %\vspace{\TThreeMoveProbB}
   }%
}
</pre></body></html>