  Let $X_1,X_2,...$ be independent identically distributed random variables
with values in $\C$. Denote by $\mu$ the probability distribution of $X_1$.
Consider a random polynomial $P_n(z)=(z-X_1)...(z-X_n)$. We prove a conjecture
of Pemantle and Rivin [arXiv:1109.5975] that the empirical measure
$\mu_n:=\frac 1{n-1}\sum_{P_n'(z)=0} \delta_z$ counting the complex zeros of
the derivative $P_n'$ converges in probability to $\mu$, as $n\to\infty$.
