# 3: Discrete Random Variables

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• 3.1: Prelude to Discrete Random Variables
Random Variable (RV) a characteristic of interest in a population being studied
• 3.2: 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.
• 3.3: 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.
• 3.4: 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.
• 3.5: Geometric Distribution
There are three characteristics of a geometric experiment: (1) There are one or more Bernoulli trials with all failures except the last one, which is a success. (2) In theory, the number of trials could go on forever. There must be at least one trial. (3) The probability, p, of a success and the probability, q, of a failure are the same for each trial. In a geometric experiment, define the discrete random variable X as the number of independent trials until the first success.
• 3.6: 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.
• 3.7: 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.
• 3.E: Discrete Random Variables (Exercises)
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.