Strong law for Poisson arrival times
= Strong law for Poisson arrival times
{title2=$Y_n/n\to1/\lambda$}
For a homogeneous <Poisson process> of rate $\lambda>0$, $N(t)/t\to\lambda$ almost surely: unit-time increments are independent Poisson variables and the <strong law of large numbers> applies, then monotonicity fills the intervals between integers. At its $n$th point $Y_n$, simplicity gives $N(Y_n)=n$. Consequently $Y_n/n\to1/\lambda$. Rate and mean interarrival time are reciprocals.