Lesson 23: Transformations of Two Random Variables

Introduction Section

In this lesson, we consider the situation where we have two random variables and we are interested in the joint distribution of two new random variables which are a transformation of the original one. Such a transformation is called a bivariate transformation. We use a generalization of the change of variables technique which we learned in Lesson 22. We provide examples of random variables whose density functions can be derived through a bivariate transformation.


Upon completion of this lesson, you should be able to:

  • To learn how to use the change-of-variable technique to find the probability distribution of \(Y_1 = u_1(X_1, X_2), Y_2 = u_2(X_1, X_2)\), a one-to-one transformation of the two random variables \(X_1\) and \(X_2\).