Definition: Expected value

Index: The Book of Statistical Proofs ▷ General 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:

• Wikipedia (2020): "Expected value"; in: Wikipedia, the free encyclopedia, retrieved on 2020-02-13; URL: https://en.wikipedia.org/wiki/Expected_value#Definition.

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