I have this Weibull density function,
$$ f(x) = 0.25 \left| 1-x \right|^{-0.5} \exp(-\left| 1-x \right|^{0.5})$$
Because of the absolute value, this is split into 2 cases.
Its cumulative function
$$F(a)=\int f(x) \; dx = \begin{cases} \frac{1}{2} e^{-\left( 1-a \right)^{0.5}} -\frac{1}{2} e^{-1} & 0 I take a=$\infty$, this cdf doesn't integrate to 1?? $$\left[1-\frac{1}{2} e^{-(a-1)^{0.5}} - \frac{1}{2} e^{-1}\right]_1^\infty = 1 - \frac{1}{2} e^{-1}$$ What is wrong?