**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.**