Expected value of a random vector

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Expected value ▷ Expected value of a random vector

Definition: Let $X$ be an $n \times 1$ random vector. Then, the expected value of $X$ is an $n \times 1$ vector whose entries correspond to the expected values of the entries of the random vector:

\[\label{eq:mean-rvec} \mathrm{E}(X) = \mathrm{E}\left( \left[ \begin{array}{c} X_1 \\ \vdots \\ X_n \end{array} \right] \right) = \left[ \begin{array}{c} \mathrm{E}(X_1) \\ \vdots \\ \mathrm{E}(X_n) \end{array} \right] \; .\]

Sources:

Taboga, Marco (2017): "Expected value"; in: Lectures on probability theory and mathematical statistics, retrieved on 2021-07-08; URL: https://www.statlect.com/fundamentals-of-probability/expected-value#hid12.
Wikipedia (2021): "Multivariate random variable"; in: Wikipedia, the free encyclopedia, retrieved on 2021-07-08; URL: https://en.wikipedia.org/wiki/Multivariate_random_variable#Expected_value.

Metadata: ID: D154 | shortcut: mean-rvec | author: JoramSoch | date: 2021-07-08, 08:34.