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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 = 15.67. 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 15.67 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 = 15.67. We know X has this distribution because the random variable 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, …}.
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Continuing the candy example, let us calculate the expected number of defective pieces of candy produced each week. That is, calculate E[X] (or μ).
In the box below, please enter the mean of the distribution given above, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
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