Solution
= Solution
The strong law gives $T_n/n\to1/\lambda$. Since $T_{N_t}\le t<T_{N_t+1}$ and $N_t\to\infty$, sandwiching yields $N_t/t\to\lambda$ almost surely.
= Solution
The strong law gives $T_n/n\to1/\lambda$. Since $T_{N_t}\le t<T_{N_t+1}$ and $N_t\to\infty$, sandwiching yields $N_t/t\to\lambda$ almost surely.