Let's say I have $60$ time intervals and I want to generate appearance of people where time between their appearances is selected using exponential distribution with parameter $\lambda$. How do I do it?
2026-03-29 16:55:53.1774803353
Exponential distribution in queue model M/M/1
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If the intervals between successive arrivals are independent and follow an $\text{Exponential}(\lambda)$ distribution, we call this a Poisson process with rate $\lambda$.
The number of arrivals in any time interval of length $t$ has the $\text{Poisson}(\lambda t)$ distribution.