= Quantile endpoint at probability one
{title2=$F^{-1}(1)=\inf\{x:F(x)=1\}$}
The <quantile function> is finite at every <probability> strictly between zero and one, but need not be finite at one. For any unbounded-above <normal distribution>, $F(x)<1$ for every real $x$, so its generalized inverse at one is $+\infty$. <Inverse transform sampling> still produces a real <random variable> <almost surely> because a continuous <uniform distribution> puts zero mass at that <endpoint>. A real-valued implementation may discard <endpoint> draws or assign an arbitrary finite value there without changing the sampled law.
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