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Beta Distribution

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Calculate the probability density function, lower cumulative distribution function, and upper cumulative distribution function of the beta distribution.
Percentile x
0≦x≦1
Shape parameter a
a＞0
Shape parameter b
b＞0
\(\normalsize Beta\ distribution\\ (1)\ probability\ density\\ \hspace{30px}f(x,a,b)={\large\frac{1}{B(a,b)}}x^{a-1}(1-x)^{b-1}\\ (2)\ lower\ cumulative\ distribution\\ \hspace{30px}P(x,a,b)={\large\int_{\small 0}^{\small x}}f(t,a,b)dt\\ (3)\ upper\ cumulative\ distribution\\ \hspace{30px}Q(x,a,b)={\large\int_{\small x}^{\small 1}}f(t,a,b)dt\\\)

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