Random Variable

• Variable - any quantity that is unknown in context of math problem - any characteristic or attribute of a population or sample under study (height, weight, temperature, age, ranking)
• Random - without definite aim, direction, rule, or method - probability or chances
• Random Variable

  • function that associates a numerical value with every outcome of an experiment, denoted by capital letter X
  • domain is a sample space/range is set of real numbers
  • can represent quantities, measurements, or characteristics of interest

  Examples:

  1. The number of children in a family {x|x≥0; x ∈ W}
  2. Number of correct answer in 20 item T or F {x|0≤x≤20; x ∈ W}
  3. Lifetime of a flashlight battery {x|x≥0 hours; x ∈ R}
• Statistics - involves the method of collecting, organizing, summarizing, analyzing, and drawing conclusions about the data to provide answers or solutions for an inquire
• Probability - exact value of chance than an event will occur
• Random Experiment - repeated numerous times under the same condition, results must be independent of one another
• Outcome - result of random experiment
• Chance - likelihood of a particular event to happen
• Sample Space - set of possible outcome of a random experiment, capital S
• Probability Distribution - for discrete random variable
• Probability Density Function - for continuous random variable