
\subsection{Covariance matrix}

With multiple events, covariance can be defined between each pair of events, including the event with itself.

The covariance between \(2\) variables is:

\(Cov(x_i,x_j):=E(x_ix_j)-E(x_i)E(x_j)\)

Which is equal to:

\(Cov(x_i,x_j)=E{[x_i-E(x_i)][x_j-E(x_j)]}\)

We can therefore generate a covariance matrix through:

\(\sum =E[(X-E[X])(X-E[X])^T]\)

