Latex expected value symbol - expectation

Expected value or expectation of a random variable $X$ is defined, if it exists, in a mathematically precise way with respect to a probability space, typically denoted as $(\mathrm{\Omega },\mathcal{A},\mathbb{P})$, where $\mathrm{\Omega }$ is the universe of possibilities, $\mathcal{A}$ the set of possible events (which are the possible values of the random variable $X$) and $\mathbb{P}$ a probability measure such that $\mathbb{P}(\mathrm{\Omega })=1$.

Latex expected value using mathbb function

To use the latex expected value using mathbb function, you must load amssymb package

\documentclass[12pt]{article}
\usepackage{amssymb}
...
\end{document}

Next, we use \mathbb function.

Here are five examples using LaTeX to write expected value of a random variable $X$ :

\documentclass[12pt]{article}
\usepackage{amssymb}
$$ \mathbb{E}[X] = \sum_{i=1}^{n} x_i \cdot p_i $$

$$ \mathbb{E}[X] = \frac{\displaystyle\sum_{i=1}^{n} x_i \cdot p_i}{\displaystyle\sum_{i=1}^{n} p_i} $$

$$ \mathbb{E}[X] = \int_{-\infty}^{\infty} xf(x) \, dx $$

$$ \mathbb{E}[X] = \frac{1}{n} \sum_{i=1}^{n} x_i $$

$$ \mathbb{E}[X] = \int_{-\infty}^{\infty} x \, dF(x) $$
\end{document}

$$\mathbb{E}[X]=\sum _{i=1}^n{x}_i\cdot p_i$$ $$\mathbb{E}[X]=\frac{{\displaystyle \sum _{i=1}^n{x}_i\cdot p_i}}{{\displaystyle \sum _{i=1}^n{p}_i}}$$ $$\mathbb{E}[X]={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}xf(x)dx$$ $$\mathbb{E}[X]=\frac{1}{n}\sum _{i=1}^n{x}_i$$ $$\mathbb{E}[X]={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}xdF(x)$$