5. Collections of Events

Most questions in data science involve multiple variables and events. Random variables and their joint distributions give us a way to set up probabilistic models for how our data originate. Some techniques are particularly useful for working with large collections of variables and events. These include:

• Using bounds when exact values are difficult to calculate

• Noticing patterns when working with small collections and then generalizing to larger ones

• Using symmetry, both for insight and for simplifying calculation

In this chapter we will study powerful examples of all these techniques.