Calculating Expected Values

The Problem Statement

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 7 taken from a population of size 43, in which there are 22 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 7 people from its workforce of 43. (In this workforce, only 22 of those 43 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 0 and 7, inclusive. In other words, S = {0, 1, 2, …, 7}.

The Probability Graphic

Here is the probability function of the Hypergeometric distribution described in the example:

To Calculate

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].

Your Answer

Another Hypergeometric Distribution

Would you like to continue working on this topic? If so, click here for another Hypergeometric distribution.

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