# Notes - Machine Learning MT23, Inverse transform sampling

### Flashcards

Suppose we want to sample from a distribution $D$. How can you achieve this with inverse transform sampling?

Sample $x$ from $U[0, 1]$. Then take $F^{-1}(x)$ where $F^{-1}$ is the inverse cumulative distribution function.

### Proofs

Prove that inverse transform sampling works, i.e. if $X \sim D$ then $Y = F _ X^{-1}(U)$ where $U \sim U[0, 1]$ has the same distribution.

Todo, http://www3.eng.cam.ac.uk/~ss248/G12-M01/Week1/ITM.pdf.