deletions | additions       diff --git a/Thanks_for_catching_this_The__.tex b/Thanks_for_catching_this_The__.tex  index a3b0793..db6a532 100644  --- a/Thanks_for_catching_this_The__.tex  +++ b/Thanks_for_catching_this_The__.tex 
...
Thanks for catching this! The formulas are now: were changed as follows:  \begin{equation}   L_1 = \prod\limits_j\frac{1}{\sqrt{2\pi a_j^2 V_j}}exp\Big(\frac{-(\beta_{1j}- \mu)^2}{2 a_j^2 V_j}\Big)