Of the following, the one that most resembles a Poisson random variable is the number of:
A)heads in 200 flips of a fair coin.
B)annual power failures at your residence.
C)face cards in a bridge hand of 13 cards.
D)defective CDs in a spool containing 15 CDs.

Question

Quizplus · Accepted Answer

Poisson random variables model the number of occurrences of rare events that happen independently and with a constant average rate over time or space. Option B, annual power failures at a particular residence, can be modeled as a Poisson random variable as power failures are rare events that happen randomly over time and are not affected by past failures. In contrast, options A and C involve events that are not independent as the outcomes of past events affect the outcomes of future events. Option D involves a finite population, which makes it more suitable for modeling with a hypergeometric distribution instead of the Poisson distribution.

Of the Following, the One That Most Resembles a Poisson