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.