Section 6.1 Selecting Randomly
When motivating our definition of probability you may have noticed that we modeled our definition on the relative frequency of equally likely 4.3.11 outcomes. You have seen that it is not necessarily true that all values of the random variable lead to equal probabilities.
You often will consider experiments that start with random selections from a known space where each remaining item at each time has the same chance as all the others of being selected. Thus, theoretical counting from the previous chapter becomes extremely important.
In this chapter, you will investigate the following distributions:
- Discrete Uniform - each of a finite collection of outcomes is equally likely and prescribed a "position" and \(X\) measures the position of an item selected randomly from the outcomes.
- Continuous Uniform - an interval of values is possible with sub-intervals of equal length having equal probabilities and \(X\) measures a location inside that interval.
- Hypergeometric - each of a finite collection of values are equally likely and grouped into two classes (successes vs failures) and a subset of that collection is extracted with \(X\) measuring the number of successes in the sample.