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.) zvalue 1.645 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.)

Pppf=0.80.80.2=0.128
1 fxi02 i=1nfxi=13 fxi=PX=xi
fx=0.038,x=10.102,x=20.172,x=30.204,x=40.174,x=50.124,x=60.080,x=70.036,x=80.028,x=90.022,x=100.020,x=15

Formula 1: $$ \begin{equation} \label{Formula1.Label} P (\Omega) = \int_{-\infty}^{+\infty} f (x) \: dx = 1 \end{equation} $$

Formula 2: $$ \begin{equation} \label{Formula2.Label} E (X) := \int_{-\infty}^{+\infty} x \: f (x) \; dx \end{equation} $$

A third one, with references to 1 and 2: $$ \begin{equation} \begin{array}{ll} E (a X + b) & = \int_{-\infty}^{+\infty} (a x - b) \: f(x) \: dx \\ \\ & = a \int_{-\infty}^{+\infty} x \: f(x) \: dx + b \int_{-\infty}^{+\infty} f(x) \: dx \\ \\ & \underset{\eqref{Formula1.Label}, \eqref{Formula2.Label}}{=} a E(X) + b \end{array} \end{equation} $$

And another one: $$ \begin{equation} V(X) = \frac{a^2 + b^2 + c^2 - ab - ac - bc}{18} \end{equation} $$