\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{}
\lhead{\resizebox{!}{2cm}{M}}
\chead{\raisebox{0.5cm}{\Huge Variance / SD}} % (add title text if you want)
\rhead{\resizebox{!}{2cm}{M}}
\setlength{\headheight}{2.5cm}
\setlength{\headsep}{12pt} % space between header and body

\begin{document}
\thispagestyle{fancy}

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

% -------- Single -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/single.png}}} 
&$X = \{1,2,3,4,5,6\}$\\
&$P(X = x) = \frac{1}{6}$\\
&\\
&\\
&\\
&\\
\end{tabular}

% -------- Abstract -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/abstract.png}}} 
&$E(X) = \sum_{x=1}^6 x \cdot \frac{1}{6} = \frac{1+2+3+4+5+6}{6} = \frac{21}{6} = 3.5$\\
&\hrule\\
&\\
&$E(X^2) = \sum_{x=1}^6 x^2 \cdot \frac{1}{6} = \frac{1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2}{6} = \frac{91}{6}$\\
&\hrule\\
&\\
&$\operatorname{Var}(X) = E(X^2) - [E(X)]^2 = \frac{91}{6} - (3.5)^2 = \frac{91}{6} - \frac{49}{4} = \frac{182 - 147}{12} = \frac{35}{12} = \frac{35}{12}$\\
&\hrule\\
&\\
&$\operatorname{SD}(X) = \sqrt{\operatorname{Var}(X)} = \sqrt{\frac{35}{12}} = \sqrt{\frac{35}{12}} \approx 1.708$\\
&\\
&$\mathrm{Var}(4X + 2) = 16\,\mathrm{Var}(X)$\\
&\\
\end{tabular}

% -------- Question -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/question.png}}} 
&$P(0 < X \leq 20) =0.06 : P(20 < X \leq 30) =0.18$\\
&$P(30 < X \leq 40) =0.26 : P(40 < X \leq 50) =0.22$\\
&$P(50 < X \leq 60) =0.14 : P(60 < X \leq 70) =0.06$\\
&$P(70 < X \leq 80) =0.04 : P(80 < X \leq 90) =0.04$\\
&$P(X > 90) =0.00$\\
&\hrule\\
&\\
&$Y(X<50) = 0 \rightarrow P(Y=0) = 0.72$\\
&$Y(50 \leq X < 60) = 300 \rightarrow P(Y=300) = 0.14$\\
&$Y(60 \leq X > 70) = 600 \rightarrow P(Y=600) = 0.06$\\
&$Y(X \geq 70) = 700 \rightarrow P(Y=700) = 0.08$\\
&\hrule\\
&\\
&$E(Y)=? : E(Y^2)=? : Var(Y)=? : \sigma_Y=?$\\
\end{tabular}
\end{table}


% second page
\newpage
\thispagestyle{fancy}
\begin{table}[h!]
% -------- Answer -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/key.png}}} 
&$P(0 < X \leq 20) =0.06 : P(20 < X \leq 30) =0.18$\\
&$P(30 < X \leq 40) =0.26 : P(40 < X \leq 50) =0.22$\\
&$P(50 < X \leq 60) =0.14 : P(60 < X \leq 70) =0.06$\\
&$P(70 < X \leq 80) =0.04 : P(80 < X \leq 90) =0.04$\\
&$P(X > 90) =0.00$\\
&\hrule\\
&\\
&$Y(X<50) = 0 \rightarrow P(Y=0) = 0.72$\\
&$Y(50 \leq X < 60) = 300 \rightarrow P(Y=300) = 0.14$\\
&$Y(60 \leq X > 70) = 600 \rightarrow P(Y=600) = 0.06$\\
&$Y(X \geq 70) = 700 \rightarrow P(Y=700) = 0.08$\\
&\hrule\\
&\\
&$E(Y)=? : E(Y^2)=? : Var(Y)=? : \sigma_Y=?$\\
&\hrule\\
&\\
&$E(Y)=0\cdot0.72+300\cdot0.14+600\cdot0.06+700\cdot0.08$\\
&$E(Y)=42+36+56$\\
&$E(Y)=134$\\
&\hrule\\
&\\
&$E(Y^2) = 0^2\cdot0.72+300^2\cdot0.14+600^2\cdot0.06+700^2\cdot0.08$\\
&$E(Y^2) = 90{,}000\cdot0.14+360{,}000\cdot0.06+490{,}000\cdot0.08$\\
&$E(Y^2) =12{,}600+21{,}600+39{,}200$\\
&$E(Y^2) = 73{,}400$\\
&\hrule\\
&\\
&$Var(Y)=E(Y^2)-\bigl[E(Y)\bigr]^2$\\
&$Var(Y)=73{,}400 - (134)^2$\\
&$Var(Y)=73{,}400 - 17{,}956$\\
&$Var(Y)=55{,}444.$\\
&\hrule\\
&\\
&$\sigma_Y = \sqrt{\Var(Y)}$\\
&$\sigma_Y = \sqrt{55{,}444}$\\
&$\sigma_Y \approx 235.5$\\
\end{tabular}
\end{table}
\end{document}