  The purpose of this note is to point out that the theory of expander graphs
leads to an interesting test whether $n$ real numbers $x_1, \dots, x_n$ could
be $n$ independent samples of a random variable. To any distinct, real numbers
$x_1, \dots, x_n$, we associate a 4-regular graph $G$ as follows: using $\pi$
to denote the permutation ordering the elements, $x_{\pi(1)} < x_{\pi(2)} <
\dots < x_{\pi(n)}$, we build a graph on $\left\{1, \dots, n\right\}$ by
connecting $i$ and $i+1$ (cyclically) and $\pi(i)$ and $\pi(i+1)$ (cyclically).
If the numbers are i.i.d. samples, then a result of Friedman implies that $G$
is close to Ramanujan. This suggests a test for whether these numbers are
i.i.d: compute the second largest (in absolute value) eigenvalue of the
adjacency matrix. The larger $\lambda - 2\sqrt{3}$, the less likely it is for
the numbers to be i.i.d. We explain why this is a reasonable test and give many
examples.
