Calculating Variances

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 9 taken from a population of size 23, in which there are 13 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 9 people from its workforce of 23. (In this workforce, only 13 of those 23 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 9, inclusive. In other words, S = {0, 1, 2, …, 9}.

The Probability Graphic

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

To Calculate

Continuing the candy example, we know that the expected number of people in the sample who like the candies is . However, it is important to determine how variable X is about this mean. So, to that end, what is the variance of X? In symbols, calculate V[X].

Your Answer

Another Hypergeometric Distribution

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

Assistance