Uniform distribution on simplex

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chowpy
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How can we show that Dirichlet distribution with parameters α = (α1, ..., αK) all equal to one is uniformly distributed on a K-dimensional unit simplex?
 
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chowpy said:
How can we show that Dirichlet distribution with parameters α = (α1, ..., αK) all equal to one is uniformly distributed on a K-dimensional unit simplex?

Isn't it true by definition?
 

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