Which distribution models the count of events in a fixed interval when the mean count is the same for each interval?

Which distribution models the count of events in a fixed interval when the mean count is the same for each interval?

• A. Binomial distribution
• B. Normal distribution
• C. Poisson distribution
• D. Uniform distribution

Answer: (C)

Counting events in a fixed interval when the average number of events is the same from one interval to the next is modeled by the Poisson distribution. This distribution suits counts that are nonnegative integers, where events occur independently and at a constant average rate. The mean per interval is a single parameter, lambda, and the same lambda applies to every identical interval, which matches the scenario of a fixed mean across intervals. Because of these properties, the Poisson model naturally describes how many events you’d expect to see in each interval. Other options don’t fit as well: the binomial needs a fixed number of trials with a success probability, the normal is for continuous outcomes or large sampled quantities, and the uniform assigns equal likelihood to a range of counts, which isn’t typical for event counts with a steady rate.

Counting events in a fixed interval when the average number of events is the same from one interval to the next is modeled by the Poisson distribution. This distribution suits counts that are nonnegative integers, where events occur independently and at a constant average rate. The mean per interval is a single parameter, lambda, and the same lambda applies to every identical interval, which matches the scenario of a fixed mean across intervals. Because of these properties, the Poisson model naturally describes how many events you’d expect to see in each interval. Other options don’t fit as well: the binomial needs a fixed number of trials with a success probability, the normal is for continuous outcomes or large sampled quantities, and the uniform assigns equal likelihood to a range of counts, which isn’t typical for event counts with a steady rate.