I computed mean, variance and covariance of the Dirichlet distribution. To do so, I computed \(E[x_k]\), \(E[x_k^2]\) and \(E[x_i x_j]\). This is the first time I've dealt with multivariate distributions. The mean should be the weighted sum of the vectors x in the simplex so I can consider one component at a time and compute \(E[x_k]\). But what is \(x^2\)? Is \(x^2 = [x_1^2, x_2^2, \ldots ,x_N^2]^T\) and so I can compute \(E[x_k^2]\) individually? And what about the covariance? Are variance and covariance about the components of the vectors x?