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5: Continuous Random Variables

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  • Continuous random variables have many applications. Baseball batting averages, IQ scores, the length of time a long distance telephone call lasts, the amount of money a person carries, the length of time a computer chip lasts, and SAT scores are just a few. The field of reliability depends on a variety of continuous random variables.

    • 5.1: Introduction
      The graph of a continuous probability distribution is a curve. Probability is represented by area under the curve. The curve is called the probability density function (abbreviated as pdf).
    • 5.2: Continuous Probability Functions
      The probability density function (pdf) is used to describe probabilities for continuous random variables. The area under the density curve between two points corresponds to the probability that the variable falls between those two values. In other words, the area under the density curve between points a and b is equal to P(a<x<b)P(a<x<b) . The cumulative distribution function (cdf) gives the probability as an area.
    • 5.3: The Uniform Distribution
      The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.
    • 5.4: The Exponential Distribution
      The exponential distribution is often concerned with the amount of time until some specific event occurs. Values for an exponential random variable occur in the following way. There are fewer large values and more small values. The exponential distribution is widely used in the field of reliability. Reliability deals with the amount of time a product lasts.
    • 5.5: Continuous Distribution (Worksheet)
      A statistics Worksheet: The student will compare and contrast empirical data from a random number generator with the uniform distribution.
    • 5.E: Continuous Random Variables (Exercises)
      These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.
    • 5.E: Exercises
      These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

    Contributors and Attributions

    • 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