# Lesson 49: Run Test and Test for Randomness

In this lesson, we'll learn how to use what is called the **Run Test** to test whether the distribution functions *F*(*x*) and *G*(*y*) of two continuous random variables *X* and *Y*, respectively, are equal. That is, we'll use the Run Test to test the null hypothesis:

\[H_0 : F(z)=G(z)\]

against any of the typical alternatives. Note that other than the requirement that the random variables be continuous, no other conditions about the distributions must be met in order for the Run Test to be an appropriate test.

We'll close the lesson with seeing one particular application of the Run Test, namely, that of testing whether a series of observations are random (as opposed to showing some trend or some cycling.)