Expectation

Last updated Nov 1, 2022

Let $(\Omega, \mathcal{B}, \mathbb{P})$ be a Probability Space and let $X$ be a Random Variable on $\Omega$. The Expectation of $X$ is defined as

$$\mathbb{E}(X) := \int\limits_{\Omega} X d \mathbb{P}(\omega)$$

so long as the right hand quantity exists. If it does not, we say $\mathbb{E}(X)$ does not exist.

• Integration