Faisal Shahzad, 30, a United States naturalized citizen from Pakistan, pleaded guilty to a failed attempt to explode a car bomb in Times Square in New York City in May 2010. Shahzad was sentenced to life in prison. (Songquan Deng/Shutterstock.) Faisal Shahzad, 30, a United States naturalized citizen from Pakistan, pleaded guilty to a failed attempt to explode a car bomb in Times Square in New York City in May 2010. Shahzad was sentenced to life in prison. (Songquan Deng/Shutterstock.)
Formula 1: $$ \begin{equation*} P (\Omega) = \int_{-\infty}^{+\infty} f (x) \: dx = 1 \end{equation*} $$
Formula 2: $$ \begin{equation*} E (X) := \int_{-\infty}^{+\infty} x \: f (x) \; dx \end{equation*} $$
A third one, with references to 1 and 2: $$ \begin{equation*} \begin{array}{ll} E (a X + b) = \int_{-\infty}^{+\infty} (a x - b) \: f(x) \: dx \\ \\ = a \int_{-\infty}^{+\infty} x \: f(x) \: dx + b \int_{-\infty}^{+\infty} f(x) \: dx \\ a E(X) + b \end{array} \end{equation*} $$
And another one: $$ \begin{equation*} V(X) = \frac{a^2 + b^2 + c^2 - ab - ac - bc}{18} \end{equation*} $$