The topic for this chapter is transformations of random variables and random vectors. After applying a function to a random variable X or random vector X, the goal is to find the distribution of the transformed random variable or joint distribution of the random vector.
Transformations of random variables appear all over the place in statistics. Here are a few examples, to preview the kinds of transformations we’ll be looking at in this chapter.
- Unit conversion: In one dimension, we’ve already seen how standardization and location-scale transformations can be useful tools for learning about an entire family of distributions. A location-scale change is linear, converting an r.v. X to the r.v. Y = aX + b where a and ...