The probability density function (pdf) of the Gamma distribution for a random variable \( X \) is given by:
\[ f(x; \alpha, \beta) = \frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-\beta x} \]
for \( x > 0 \), \( \alpha > 0 \) (shape parameter), and \( \beta
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