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For a Dirichlet variable, I know the means and covariances, that is,

[itex] E[X_i] = \alpha_i/\alpha_0 [/itex]

[itex] Cov[X_i,X_j] = \frac{ \alpha_i (\alpha_0I[i=j] - \alpha_j)}{\alpha_0^2(\alpha_0 + 1)}[/itex]

But how can I prove these facts?

[itex] E[X_i] = \alpha_i/\alpha_0 [/itex]

[itex] Cov[X_i,X_j] = \frac{ \alpha_i (\alpha_0I[i=j] - \alpha_j)}{\alpha_0^2(\alpha_0 + 1)}[/itex]

But how can I prove these facts?

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