What is a key feature of the Poisson distribution?

The Poisson distribution is fundamentally about modeling the number of events that happen within a fixed interval of time or space. One key feature of this distribution is its focus on events that occur over a specified period, which means it is particularly useful for understanding phenomena like the number of phone calls at a call center in an hour, or the number of emails received in a day.

This characteristic captures the essence of how Poisson processes operate: they measure the likelihood of a certain number of events happening in a designated period or area, provided that these events are rare relative to the length of the interval being considered.

While the other options touch upon some truths related to the Poisson distribution, they do not encapsulate its defining feature as clearly. For instance, the distribution does apply to discrete data, but it is most notable for the time or space aspect. Independence of trials is an assumption made in many uses of the Poisson process, but again, it’s not the most distinguishing characteristic. Lastly, while the Poisson distribution does indeed involve average outcomes, it is more accurate to say it’s about modeling specific occurrences within those outcomes. Therefore, the focus on event occurrences within given intervals is what truly characterizes the Poisson distribution.