Henrique was spot on: we were missing r1 and r2

Author: maxbiostat

assignments/warmup_assignment.pdf

@@ -46,7 +46,7 @@ \section*{Questions}
  Show that the average distance between $x_1$ and $x_2$ is $s/3$.
  \item Show that Problem A is equivalent to computing
  \begin{equation*}
-  I = \frac{1}{\pi^2 R^4}\int_{0}^{R}\int_{0}^{R}\int_{0}^{2\pi}\int_{0}^{2\pi}\sqrt{r_1^2 + r_2^2 - 2r_1r_2\cos\phi(\theta_1, \theta_2)}\,d\theta_1\,d\theta_2\,dr_1\,dr_2,
+  I = \frac{1}{\pi^2 R^4}\int_{0}^{R}\int_{0}^{R}\int_{0}^{2\pi}\int_{0}^{2\pi}\sqrt{r_1^2 + r_2^2 - 2r_1r_2\cos\phi(\theta_1, \theta_2)}r_1r_2\,d\theta_1\,d\theta_2\,dr_1\,dr_2,
  \end{equation*}
  where $\phi(\theta_1, \theta_2)$ is the central angle between $r_1$ and $r_2$.