\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}{P}} 
\chead{%
  \raisebox{0.2cm}{%
    \shortstack{\Huge Hyper-geometric\\ \Huge Random Variable}%
  }%
}
\rhead{\resizebox{!}{1.5cm}{P}}

\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}}} 
&$N = 5$\\
&$K = 2$\\
&$n = 2$\\
&$k = 1$\\
&\\
\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}}} 
&$P(X = k)= \frac{\displaystyle\binom{K}{k}\binom{N-K}{n-k}}{\displaystyle\binom{N}{n}}$\\
&\\
&$P(X=1)= \frac{\displaystyle\binom{2}{1}\binom{3}{1}}{\displaystyle\binom{5}{2}}= \displaystyle\frac{2 \times 3}{10}= \displaystyle\frac{6}{10}= \displaystyle\boxed{0.6}$\\
&\hrule\\
&\\
&$E[X] = \displaystyle n\frac{K}{N}$\\
&\hrule\\
&\\
&$\displaystyle{\mathrm{Var}(X)} \;=\;n\frac{K}{N}\Bigl(1-\frac{K}{N}\Bigr)\frac{N-n}{\,N-1\,} $\\
&\\
\end{tabular}
\par\noindent\rule{\linewidth}{1.2pt}\par
% -------- Question -------------------
\begin{tabular}{m{1.2in} m{4in}}
\\
\multirow{4}{*}{\fbox{\includegraphics[width=1in]{images/question.png}}} 
&$N=25$\\
&$K=5$\\
&$n=10$\\
&$E[X] = ?$\\
&$\mathrm{Var}(X)=?$\\
&$\sigma_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}}} 
&$N=25$\\
&$K=5$\\
&$n=10$\\
&$E[X] = ?$\\
&$\mathrm{Var}(X)=?$\\
&$\sigma_X = ?$\\
&\hrule\\
&\\
&$E[X] = n \displaystyle\frac{K}{N} = 10\cdot\frac{5}{25} = \boxed{2}$\\
&\hrule\\
&\\
&$\mathrm{Var}(X)= n\,\displaystyle\frac{K}{N}\,\displaystyle\Bigl(1-\frac{K}{N}\Bigr)\,\displaystyle\frac{N-n}{N-1}$\\
&\\
&$\mathrm{Var}(X)=10\cdot\displaystyle\frac{5}{25}\cdot\displaystyle\frac{20}{25}\cdot\displaystyle\frac{15}{24}$\\
&\\
&$\mathrm{Var}(X)=\boxed{1}$\\
&\hrule\\
&\\
&$\sigma_X = \sqrt{\mathrm{Var}(X)} = \boxed{1}$\\
\end{tabular}
\end{table}
\end{document}