For functions that are not monotonic, the probability density function for y is ∑ ∑ k = 1 n ( y ) | d d y g k − − 1 ( y ) | ⋅ ⋅ f X ( g k − − 1 ( y ) ) , where n (y) is the number of solutions in x for the equation g ( x ) = y , and g k − − 1 ( y ) are these solutions.