The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Which of the following discrete probability distributions' properties are satisfied by random variable x?
A) Normal
B) Poisson
C) Binomial
D) Hypergeometric

Question

Quizplus · Accepted Answer

The random variable x represents the number of occurrences in a fixed interval of time and the probability of an event occurring is the same in any two-time periods of equal length. These are the defining characteristics of a Poisson distribution. Additionally, the mean of the Poisson distribution is equal to lambda, which in this case is 5.3 occurrences per ten minutes.

The Random Variable X Is the Number of Occurrences of an Event