Solution
= Solution
{c}
The unit-time increments $D_j=N_j-N_{j-1}$ are <independent and identically distributed random variables>, by <independent increments> and <stationary increments> of the <Poisson process>. Each has the <Poisson distribution> of parameter one, hence <expected value> one and <variance> one. The <central limit theorem> therefore gives
$$
\boxed{\frac{N_n-n}{\sqrt n}=\frac1{\sqrt n}\sum_{j=1}^n(D_j-1)\ \xrightarrow{\mathrm d}\ N(0,1).}
$$