# 4: Discrete Random Variables

- Page ID
- 6916

- 4.1: Prelude to Discrete Random Variables
- Random Variable (RV) a characteristic of interest in a population being studied

- 4.2: Probability Distribution Function (PDF) for a Discrete Random Variable
- A discrete probability distribution function has two characteristics: Each probability is between zero and one, inclusive. The sum of the probabilities is one.

- 4.3: Mean or Expected Value and Standard Deviation
- The expected value is often referred to as the "long-term" average or mean. This means that over the long term of doing an experiment over and over, you would expect this average. This “long-term average” is known as the mean or expected value of the experiment and is denoted by the Greek letter μμ . In other words, after conducting many trials of an experiment, you would expect this average value.

- 4.4: Binomial Distribution
- A statistical experiment can be classified as a binomial experiment if the following conditions are met: (1) There are a fixed number of trials. (2)There are only two possible outcomes: "success" or "failure" for each trial. (3) The trials are independent and are repeated using identical conditions. The outcomes of a binomial experiment fit a binomial probability distribution.

- 4.5: Discrete Distribution (Playing Card Experiment)
- A statistics Worksheet: The student will compare empirical data and a theoretical distribution to determine if an everyday experiment fits a discrete distribution. The student will demonstrate an understanding of long-term probabilities.

- 4.6: Discrete Distribution (Lucky Dice Experiment)
- A statistics Worksheet: The student will compare empirical data and a theoretical distribution to determine if a Tet gambling game fits a discrete distribution. The student will demonstrate an understanding of long-term probabilities.

- 4.E: Discrete Random Variables (Exercises)
- These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

## Contributors

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/30189442-699...b91b9de@18.114.