Which statement correctly identifies the Poisson process property?

Which statement correctly identifies the Poisson process property?

• A. Normal distribution.
• B. Independence and constant rate.
• C. Exponential distribution.
• D. Dependency and variable rate.

Answer: (B)

Independence and constant rate are the defining features of a Poisson process. In this model, the numbers of events in disjoint time intervals do not influence each other (independence), and the expected count grows proportional to the length of the interval (constant rate, often denoted by lambda). This combination implies that the count in any interval of length t follows a Poisson distribution with mean lambda t, and the waiting (interarrival) times between events are independent and exponentially distributed with rate lambda. The other options don’t capture the process as a whole: a normal distribution describes a different shape for counts and isn’t the fundamental property of a Poisson process; the exponential distribution is related to interarrival times, not the overall process property itself; and “dependency and variable rate” contradicts the essential independence and constant-rate nature.

Independence and constant rate are the defining features of a Poisson process. In this model, the numbers of events in disjoint time intervals do not influence each other (independence), and the expected count grows proportional to the length of the interval (constant rate, often denoted by lambda). This combination implies that the count in any interval of length t follows a Poisson distribution with mean lambda t, and the waiting (interarrival) times between events are independent and exponentially distributed with rate lambda.

The other options don’t capture the process as a whole: a normal distribution describes a different shape for counts and isn’t the fundamental property of a Poisson process; the exponential distribution is related to interarrival times, not the overall process property itself; and “dependency and variable rate” contradicts the essential independence and constant-rate nature.