To obtain the [[Derived Distributions|derived distribution]] $Y$ from a transformation function $g(X)$, we can proceed as follows: 1. Express the [[Cumulative Density Function|CDF]] of $Y$ but expressed in terms of $X$: $ F_Y(y)=\mathbf P(Y \leq y) = \mathbf P(g(X) \leq y) $ 2. Differentiate the CDF to find the [[Probability Density Function|PDF]]: $ f_y(y)= \frac{dF_Y}{dy}(y) $ > [!note:] > This approach is more general than the ones proposed for the special cases of [[Linear Functions of Random Variables]] or [[Monotonic Functions of Random Variables]].