Start with a random variable with a known pdf.  If we use a monotone function to transform the random variable, most students who have taken a probability or first-semester statistical theory course know how to express the pdf for the transformed random variable. What do we do if the transformation is not monotone?

To answer this question, we have two resources:

  • Nicholas McMullen and Daniel Ochoa (former students at Macalester College) prepared this guide
  • Maria Bell and Jensen Stanton (students at the University of St. Thomas) prepared this Youtube video.