Part One: Probability

The Rare Event Approach

The Rare Event Approach is a way of thinking about the relationship between Rare

Events and Random Samples. This approach will be useful to us later in the course.

Suppose we have an experiment, which we use to generate random samples, and suppose further that we have a particular event, denoted E, which might be rare. We will evaluate the rarity of the event E using a random sample.

We can state the Rare Event Assumption (REA) as follows:

The probability of observing event E is approximately 0.

If the REA holds true, then it is not likely that any single random sample will exhibit the event E…

So, suppose that we have a random sample, and suppose further that the sample exhibits the event E.

Then either the REA holds true, and we have observed an exceptionally rare random sample; or the REA does not hold, and it is not unusual for any single random sample to exhibit the event E.