Which of the following correctly describes a Poisson random variable?
A) It does not generate a binomial either/or outcome because only a single type of outcome or "event" is occurring during the Poisson process.
B) It is not confined to a fixed number of trials, because its value can equal any discrete integer between zero and infinity, along a continuum of time or space.
C) It equals the number of occurrences of a specified event within a specified time or space.
D) All of these.
E) None of these.

Question

Quizplus · Accepted Answer

A) is partially correct, as it is true that only a single type of outcome or "event" is occurring during the Poisson process, but this does not necessarily mean it cannot generate a binomial either/or outcome.
B) is also partially correct, as Poisson random variables are not confined to a fixed number of trials, but its value can only equal a discrete integer between zero and infinity along a continuum of time or space, not any integer.
C) is correct, as a Poisson random variable equals the number of occurrences of a specified event within a specified time or space.
Therefore, the correct answer is D, as all three options describe features of Poisson random variables.

Which of the Following Correctly Describes a Poisson Random Variable