  The distribution of descents in fixed conjugacy classes of $S_n$ has been
studied, and it is shown that its moments have interesting properties. Kim and
Lee showed, by using Curtiss' theorem and moment generating functions, how to
prove a central limit theorem for descents in arbitrary conjugacy classes of
$S_n$. In this paper, we prove a modified version of Curtiss' theorem to shift
the interval of convergence in a more convenient fashion and use this to show
that the joint distribution of descents and major indices is asymptotically
bivariate normal.
