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Hypergeometric Distributions
Let X be a random variable following a Hypergeometric distribution. All Hypergeometric distributions have three parameters: sample size, population size, and number of successes in the population. For this problem, let X be a sample of size 5 taken from a population of size 25, in which there are 23 successes. An example of where such a distribution may arise is the following:
Statistics, Inc., wants to determine how well people like its candies. To determine this, they randomly select 5 people from its workforce of 25. (In this workforce, only 23 of those 25 actually like the candies.) Let X be the number of employees surveyed who like the candies.
From the description, we can tell that X has a Hypergeometric distribution. We know this because X is the number of successes in a finite population where subjects are not be measured more than once (i.e., “without replacement”).
For those who like pictures, here is a graphic of the probability mass function of X. Note that it has a negative skew (left skew), that its sample space is integers between 3 and 5, inclusive. In other words, S = {3, 4, 5}.
Here is the probability function of the Hypergeometric distribution described in the example:
Continuing the candy example, let us determine the expected value of X, the number of people in the survey who respond that they like the candies. In symbols, calculate E[X].
In the box below, please enter the value of E[X], where X ~ H(n=5, N=25, K=23), then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
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