$X=\sum_{i=1}^{n^2} X_{i}$ random variable. $E[X]=\frac{n^2}{a(n)}$.
For which $a$, $X \geq n\cdot C$ holds with high probability? So the following: $P(X\geq n\cdot C)= 1-o(1)$.
What would be an approach for that problem?
(To get a feeling I solved $\frac{n^2}{a}>nC$ and get a < n/C, how to proceed from here?)