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Let \(\alpha\) and \(\beta\) be positive numbers. A random variable X has the gamma distribution with parameters \(\alpha\) and \(\beta\) if X has a continuous distribution for withc the p.d.f is \[f(x|\alpha,\beta)=\begin{cases} \frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha - 1}e^{-\beta x}\quad \mathrm{for}\, x>0,\\ 0\quad \mathrm{for}\, x\le 0 \end{cases}\]