5 - Hypergeometric Distributions
Published online by Cambridge University Press: 05 June 2012
Summary
INTRODUCTION
Definition
In engineering, an experimental event (here called a trial) is often constrained to admit only two possible outcomes, usually labeled success s and failure f.
For example, a randomly chosen product specimen is classified, upon inspection, as defective or nondefective. In a destructive performance test, a prototype survives or it fails. (See also Section 4.2.)
Suppose the engineer contemplates a sequence of n such trials. If the population, from which the sample sequence is randomly chosen, is of finite size N, then it will contain some number M of items that would each produce a trial success s. The number x of successes s that could turn up in the sample sequence may then be of interest to the engineer.
Suppose, for example, a product shipment consists of N = 100 pieces. There will be 0 ≤ M ≤ N defectives in that shipment. If a random sample of size n = 15 specimens is inspected, the number x of defectives found in that sample gives the engineer information on the quality of the shipment.
The above experimental situation is characterized by the following conditions:
The sampled population is of finite size N.
A sample of n < N trials is randomly selected.
Each trial admits only two outcomes: s or f.
There are 0 ≤ M ≤ N successes s in the population.
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- Statistical Distributions in Engineering , pp. 60 - 69Publisher: Cambridge University PressPrint publication year: 1999