Definition: Expected value of a random matrix

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

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

\[\label{eq:mean-rmat} \mathrm{E}(X) = \mathrm{E}\left( \left[ \begin{array}{ccc} X_{11} & \ldots & X_{1p} \\ \vdots & \ddots & \vdots \\ X_{n1} & \ldots & X_{np} \end{array} \right] \right) = \left[ \begin{array}{ccc} \mathrm{E}(X_{11}) & \ldots & \mathrm{E}(X_{1p}) \\ \vdots & \ddots & \vdots \\ \mathrm{E}(X_{n1}) & \ldots & \mathrm{E}(X_{np}) \end{array} \right] \; .\]

 

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#hid13.

Metadata: ID: D155 | shortcut: mean-rmat | author: JoramSoch | date: 2021-07-08, 08:42.