You are here: Project Scarlet » Probability and Distributions » Poisson Distribution » Variance
Poisson Distributions
Let X be a random variable following a Poisson distribution. All Poisson distributions have just one parameter: average rate, λ (lambda). For this problem, let X have rate parameter λ = 8.33. An example of where such a distribution may arise is the following:
Statistics, Inc., makes candy. Unfortunately, they are not too good at it. Every week, an average of 8.33 pieces are defective. These defective pieces will not kill a person, but they will cause the person’s left index finger to turn scarlet. Let X be the number of defective pieces of candy manufactured in a specified week.
From the description, we can tell that X has a Poisson distribution with rate parameter λ = 8.33. We know this because X is the number of successes measured over time (or space).
For those who like pictures, here is a graphic of the probability mass function of X. Note that it is skewed positive (right), that its sample space is non-negative, and that there is no upper bound to its sample space. In other words, S = {0, 1, 2, …}.
…
Continuing the candy example, let us calculate the variance of the number of defective pieces of candy produced each week. That is, calculate V[X] (or σ²).
In the box below, please enter the variance of the distribution given above, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
Show Formula
Show Solution
© Ole J. Forsberg, Ph.D. 2024. All rights reserved. | . | |