### MathML Equations

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.)

$P\left(\mathit{ppf}\right)=\left(0.8\right)\left(0.8\right)\left(0.2\right)=0.128$
$\begin{array}{l}{A}_{i}=\sum _{j=1}^{b}{w}_{j}{\mu }_{ij}={\mu }^{0}+{\alpha }_{i}^{0}+\sum _{j}{w}_{j}{\beta }_{j}^{0},\phantom{\rule{0.5em}{0ex}}i=1,\dots ,\phantom{\rule{0.25em}{0ex}}a,\\ {B}_{j}=\sum _{i=1}^{a}{v}_{i}{\mu }_{ij}=\phantom{\rule{0.25em}{0ex}}{\mu }^{0}+\sum _{i}{v}_{i}{\alpha }_{i}^{0}+{\beta }_{j}^{0},\phantom{\rule{0.5em}{0ex}}j=1,\dots ,\phantom{\rule{0.25em}{0ex}}b,\\ \mu ={\mu }^{0}+\sum _{i}{v}_{i}{\alpha }_{i}^{0}+\sum _{j}{w}_{j}{\beta }_{j}^{0}\end{array}$

### Tex Equations

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