= Solution
{c}
Set $T_0=0$ and $E_j=T_j-T_{j-1}$. The <Poisson interarrival times> $E_j$ are <independent and identically distributed random variables> with the rate-one <exponential distribution>. In particular, $\mathbb EE_j=1$ and $\operatorname{Var}(E_j)=1$, so the finite, positive <variance> hypothesis of the <central limit theorem> holds. Since $T_n=\sum_{j=1}^nE_j$,
$$
\boxed{\frac{T_n-n}{\sqrt n}=\frac1{\sqrt n}\sum_{j=1}^n(E_j-1)\ \xrightarrow{\mathrm d}\ N(0,1).}
$$
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