Random Vector

Topics: Probability

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(definition)

Let $X_1,\dots ,X_n$ be real random variables (i.e. $X_i:\Omega \to \mathbb{R}$, $\forall i$).

The corresponding random vector (of dimension $n$) is defined as the following function:

$$(X_1,\dots ,X_n):\Omega \to {\mathbb{R}}^n$$

Just like random variables, random vectors have a (joint) density function. Additionally, we can also define marginal and conditional density functions.