# Dirichlet distribution

#### Kiuhnm

##### New Member
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?

#### BGM

##### TS Contributor
There do have component-wise operation, but in many occasion you will not consider $$\mathbf{X}^2$$ where $$\mathbf{X}$$ is not a square matrix.

When you are dealing with the multivariate distribution, you will consider the variance-covariance entry, with the $$(i, j)$$-th entry being $$Cov[X_i, X_j]$$.

#### Kiuhnm

##### New Member
I'm not sure I understand your answer completely. Maybe I should just look up the definitions of mean, variance and covariance for multivariate distributions.

Edit: OK, I think I understand now. $$E[x] = [E[x_1], \ldots, E[x_n]]^T$$ and then there is the covariance matrix. Bottom line, we can compute a component/entry at a time.

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