Index: The Book of Statistical ProofsGeneral Theorems ▷ Probability theory ▷ Expected value ▷ Definition

Definition:

1) The expected value (or, mean) of a discrete random variable $X$ with domain $\mathcal{X}$ is

$\label{eq:mean-disc} \mathrm{E}(X) = \sum_{x \in \mathcal{X}} x \cdot f_X(x)$

where $f_X(x)$ is the probability mass function of $X$.

2) The expected value (or, mean) of a continuous random variable $X$ with domain $\mathcal{X}$ is

$\label{eq:mean-cont} \mathrm{E}(X) = \int_{\mathcal{X}} x \cdot f_X(x) \, \mathrm{d}x$

where $f_X(x)$ is the probability density function of $X$.

Sources:

Metadata: ID: D11 | shortcut: mean | author: JoramSoch | date: 2020-02-13, 19:38.