Definition:Expectation of Random Vector

Definition

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

Let $\mathbf X = \tuple {X_1, X_2, \ldots, X_n}$ be a random vector.

Then the expected value of $\mathbf X$, $\expect {\mathbf X}$, is defined by:

$\expect {\mathbf X} = \tuple {\expect {X_1}, \expect {X_2}, \ldots, \expect {X_n} }$