\documentclass[12pt]{article}
\usepackage{amsmath, amssymb, graphicx, array, fancyhdr, unicode-math, multirow}

\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\sd}{SD}
\DeclareMathOperator{\Pois}{Pois}
\DeclareMathOperator{\Bin}{Bin}
\DeclareMathOperator{\NegBin}{NegBin}
\DeclareMathOperator{\sech}{sech}


% Text: Calibri, all bold
\setmainfont{Calibri}
\renewcommand{\seriesdefault}{b}

% Math: choose a math font and visually embolden it
\setmathfont{TeX Gyre Termes Math}                  % base math font
\setmathfont[FakeBold=1.9]{TeX Gyre Termes Math}    % embolden; adjust 1.6–2.4

% header
\pagestyle{fancy}
\fancyhf{}
\renewcommand{\headrulewidth}{0pt}   % <-- removes first line

\lhead{\resizebox{!}{1.5cm}{O}} 
\chead{%
  \raisebox{0.2cm}{%
    \shortstack{\Huge Negative Binomial\\ \Huge Random Variable}%
  }%
}
\rhead{\resizebox{!}{1.5cm}{O}}

\setlength{\headheight}{1cm}
\setlength{\headsep}{12pt}

\begin{document}
\par\noindent\rule{\linewidth}{1.2pt}\par
\thispagestyle{fancy}

% -------- PAGE 1 --------
\begin{table}[h!]
  \renewcommand{\arraystretch}{1.2}

% -------- Single -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{4}{*}{\fbox{\includegraphics[width=1in]{images/single.png}}} 
&$ p = 0.5$\\
&$ r = 2$\\
&$ n = 3$\\
&$ P(X = n)= \binom{n-1}{r-1}p^r(1-p)^{n-r}$\\
&$ P(X = 3)=?$\\
&\\
\end{tabular}
\par\noindent\rule{\linewidth}{1.2pt}\par
% -------- Abstract -------------------
\begin{tabular}{m{1.2in} m{4in}}
\\
\multirow{4}{*}{\fbox{\includegraphics[width=1in]{images/abstract.png}}} 
&$P(X=3)=\binom{3-1}{2-1}(0.5)^2(0.5)^{3-2}$\\
&$ P(X=3)=\binom{2}{1}(0.5)^3$\\
&$ P(X=3)=2 \times 0.125$\\
&$P(X=3)=\boxed{0.25}$\\
&\\
\end{tabular}
\par\noindent\rule{\linewidth}{1.2pt}\par
% -------- Question -------------------
\begin{tabular}{m{1.2in} m{4in}}
\\
\multirow{4}{*}{\fbox{\includegraphics[width=1in]{images/question.png}}} 
&$p=0.20$\\
&$r=3$\\
&$E[X]=?$\\
&$Var(X)=?$\\
\end{tabular}
\end{table}


% second page
\newpage
\thispagestyle{fancy}
\par\noindent\rule{\linewidth}{1.2pt}\par
\begin{table}[h!]
% -------- Answer -------------------
\begin{tabular}{m{1.2in} m{4in}}
\\
\multirow{4}{*}{\fbox{\includegraphics[width=1in]{images/key.png}}} 
&$p=0.20$\\
&$r=3$\\
&$E[X]=?$\\
&$Var(X)=?$\\
&\hrule\\
&\\
&$E[X] =\frac{r}{p}$\\
&\\
&$E[X] =\frac{3}{0.2}$\\
&\\
&$E[X] =15$\\
&\hrule\\
&\\
&$\Var(X) =\frac{r\,(1-p)}{p^2}$\\
&\\
&$\Var(X) =\frac{3\,(1-0.2)}{0.2^2}$\\
&\\
&$\Var(X) =\frac{3\cdot0.8}{0.04}$\\
&\\
&$\Var(X) =\frac{2.4}{0.04}$\\
&\\
&$\Var(X) =60$\\
\end{tabular}
\end{table}
\end{document}