Definition:Expectation of Random Vector

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Definition

Let $X_1, X_2, \ldots, X_n$ be random variables on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.

Let $\mathbf X = \left({X_1, X_2, \ldots, X_n}\right)$ be a random vector.


Then the expected value of $\mathbf X$, $\mathbb E \left[{\mathbf X}\right]$, is defined by:

$\mathbb E \left[{\mathbf X}\right] = \left({\mathbb E \left[{X_1}\right], \mathbb E \left[{X_2}\right], \ldots, \mathbb E \left[{X_n}\right]}\right)$