# Exercise C.4.4

Show that value of the maximum of the binomial distribution $b(k;n,p)$ is approximately $1/\sqrt{2 \pi n p q}$ where $q = 1 - p$.

There is a lot of calculation to be performed here, but this is essentially an application of the de Moivre-Laplace theorem. It's too complex for me to want to bother to write it down.