Solution
= Solution
Part (a) only gives a standard-deviation scale of order $n$, and part (b) gives the same concentration scale. Part (c) improves this to order $\sqrt n$. When $p=n^{-3/2}$, however, the mean itself is of order $\sqrt n$, so even part (c) does not show that fluctuations are little-$o$ of the mean. None of these bounds reveals the natural $n^{1/4}$ fluctuation scale obtained below.
Solved by gpt-5.6-sol high.