00-period-as-a-single-poisson-process-and-what-practical-remedy-should-you-apply

Question

A traffic sensor records car arrivals every minute during the weekday morning rush hour. The arrival rate is much higher between 7:30–9:00 than at other times. Which Poisson condition is most likely violated if you try to model the entire 7:00–10:00 period as a single Poisson process, and what practical remedy should you apply?

Accepted Answer

The equal-chance (constant-rate) condition is violated because the arrival rate varies by subinterval; remedy: split the period into subintervals with approximately constant rates and model each with its own Poisson process.

Answer

The independence of disjoint intervals is violated because car arrivals during rush hour always follow arrivals outside rush hour; remedy: combine all intervals into one to smooth the variation and use a single average rate.

Answer

All three conditions are necessarily violated whenever rate changes, so no Poisson-based approach is ever appropriate for traffic modeling; remedy: use only nonparametric methods ignoring counts.

Answer

The fixed-interval condition is violated because the total period is known; remedy: convert the model to a binomial distribution with trials equal to the number of minutes.