Let S be the number of successes in n independent Bernoulli trials, with possibly different probabilities $p_1, ..., p_n$ on different trials. Show that for fixed $\mu=E(S)$, $Var(S)$ is largest in case the probabilities are all equal.
I figured out that $Var(S)=\sum_{i=1}^n p_i(1-p_i)$, and my question is why $p_i$ for i=1,2,..,n are all equal to make $Var(S)$ largest.
Thanks!