# 4: Discrete Random Variables


• 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 μ . 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 gambling game fits a discrete distribution. The student will demonstrate an understanding of long-term probabilities.
• 4.7: Discrete Random Variables (Exercises)
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.