The probability density function (pdf) of a Weibull distribution is given by:
$$
f(x;\alpha,\beta) = \frac{\beta}{\alpha} \left(\frac{x}{\alpha}\right)^{\beta-1} e^{-(x/\alpha)^\beta}
$$
where $x > 0$, $\alpha > 0$ is the scale parameter, and $\beta > 0$ is the
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