Why does i-th row of P, follow a Dirichlet distribution?

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Adesupo Akinrefon

I think if you read up on mixture models you might get some insight...but the dirichlet distribution is a multivariate beta distribution. the dirichlet distribution is a conjugate pair when you have a multinomial distribution.

Oluwafemi Samson Balogun

I also agree with Akinferon

André François Plante

Samuel Wilks textbook on Mathematical Statistics (Wiley, 1962) has a section on Dirichlet distribution.