\begin{aligned}&
\textcolor{orange}{k}=\textmd{no. of trials}\\&
\textcolor{blue}{p}=\textmd{probability}
\end{aligned}Probability Mass Function
\begin{aligned} P(X=\textcolor{orange}{k})=\textcolor{blue}{p}(1-\textcolor{blue}{p})^{\textcolor{orange}{k}-1} \end{aligned}Cumulative Distribution Function
\begin{aligned} &P(X\leq\textcolor{orange}{k})=1-(1-\textcolor{blue}{p})^{\textcolor{orange}{k}} \\ \\ &
P(X \geq \textcolor{orange}{k})=(1-\textcolor{blue}{p})^{\textcolor{orange}{k}-1}
\\ \\&
P(X > \textcolor{orange}{k})=1-P(X\leq\textcolor{orange}{k})=(1-\textcolor{blue}{p})^{\textcolor{orange}{k}}
\end{aligned}Mean
\begin{aligned} &\mu =E(X)=\frac{1}{\textcolor{blue}{p}}
\end{aligned}Variance
\begin{aligned} \sigma^2=V(X)=\frac{(1-\textcolor{blue}{p})}{\textcolor{blue}{p}^2}
\end{aligned}Standard Deviation
\begin{aligned} \sigma=\sqrt{\sigma^2}
\end{aligned}
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