Probability distributions are explanations of the probabilities that a random process will result in each of the possible specific outcomes. For instance, the probability distribution of a single roll of a standard die might look like:

- 1: 16.7%
- 2: 16.7%
- 3: 16.7%
- 4: 16.7%
- 5: 16.7%
- 6: 16.7%

Different types of probability measures require different probability distributions. Continuous random variables, for instance, have an infinite number of possible outcomes in any given interval, making it impossible to create a list of individual probabilities like the ones for the die above. In this chapter, you will learn how to create and interpret all kinds of probability distributions.

## Chapter Outline

- 7.1. Understanding Discrete Random Variables
- 7.2. Understanding Continuous Random Variables
- 7.3. Probability Distribution
- 7.4. Visualizing Probability Distribution
- 7.5. Probability Density Function
- 7.6. Binomial Experiments
- 7.7. Expected Value
- 7.8. Random Variable Variance
- 7.9. Transforming Random Variables I
- 7.10. Transforming Random Variables II

### Chapter Summary

Students were introduced to the concepts of random variables and probability distributions. Instruction and exercises were provided to familiarize students with the interpretation and construction of various probability distribution tables and graphs. Binomial experiments were introduced, as were transformations of discrete random variables.