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The probability density function for a beta distribution with parameters a and b (a, b > 0) is of the form:B(x; a, b) = c*x*(a-1)*(1-x)(b-1) where 0 <= x <= 1.

c is a constant such that the integral is 1 and it can be shown that c = G(a+b)/[G(a)*G(b)] where G is the Gamma function.

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Q: What is the beta distribution formula?
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Is the beta distribution is a special case of dirichlet distribution?

In a sense.Beta distributions are the marginal distributions of the Dirichlet distribution.


Is the beta distribution closed under convex combinations viz is the convex combination of two or more beta distributions also a beta distribution?

No. For a convex combination of distributions, the density is also a convex combination of the individual densities and one can easilly check that the convex combination of beta densities is not again a beta density.


What is the difference between beta and normal distribution?

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What is the formula for finding probabilities?

The formula for finding probability depends on the distribution function.


What does unimodal mean?

Please consider the probability density function graphs for the beta distribution, given in the link. For alpha=beta=2, the density is unimodal, which is to say, it has a single maximum. In contrast, for alpha=beta=0.5, the density is bimodal; it has two maxima.