Random vector

Summary

• \(X_1,X_2, \ldots ,X_n\) are \(n\) random variables. We can collect these random variables in an \(n×1\) random vector denoted by \(X\) ,

\[X= \begin{bmatrix}X_1 \\ X_2 \\ ⋮ \\ X_n\end{bmatrix} \]

• If \(X\) is an \(n×1\) random vector then the expected value of \(X\) , denoted by \(E\left( X \right)\) , is defined as the \(n×1\) vector of constants,

\[E\left( X \right)= \begin{bmatrix}E\left( X_1 \right) \\ E\left( X_2 \right) \\ ⋮ \\ E\left( X_n \right)\end{bmatrix} \]

• The expected value of a random vector, \(E\left( X \right)\) , is often denoted by \(\mu\) .
• A more complete introduction to random vectors.