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== Intuition ==
From <math>U \sim \mathrm{Unif}[0,1]</math>, we want to generate <math>X</math> with [[Cumulative distribution function|CDF]] <math>F_X(x).</math> We assume <math>F_X(x)</math> to be a strictly increasing function, which provides good intuition.
We want to see if we can find some strictly monotone transformation <math>T:[0,1]\mapsto \mathbb{R}</math>, such that <math>T(U)\overset{d}{=}X</math>. We will have
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