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3: Probability

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    47231
    • Franz S. Hover and Michael S. Triantafyllou
    • Massachusetts Institute of Technology via MIT OpenCourseWare

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    • 3.1: Events
      Definition of events, and explanation of the difference between simple and composite events.
    • 3.2: Conditional Probability
      Explanation of composite probability, and equations for describing situations involving composite probability.
    • 3.3: Bayes' Rule
      Overview of Bayes' Rule and its applications in finding the probability of a simple event conditioned on a composite one, using the probability of the composite event conditioned on the simple one.
    • 3.4: Random Variables
      The role of the random variable \(x\) in situations where each event in a sample space is assigned a numerical value, including in finding the mean value and variance.
    • 3.5: Continuous Random Variables and the Probability Density Function
      Introduction to continuous random variables, which require the use of the probability density function to find the mean value of the random variable \(x\) and of its functions.
    • 3.6: The Gaussian PDF
      Overview of the normal, or Gaussian, probability density function
    • 3.7: The Cumulative Probability Function
      The Cumulative Probability Function, how it relates to the probability density function, and its role in transforming the pdf of a random variable into the pdf of a function of that random variable.
    • 3.8: Central Limit Theorem
      The Central Limit Theorem as a property of random variables, and a brief overview of its real-world applications. A rather amazing property of random variables is captured in the central limit theorem; that a sum of random variables taken from distributions - even many different distributions - approaches a single Gaussian distribution as the number of samples gets large.

    This page titled 3: Probability was last modified on Fri, 23 Apr 2021 05:53:01 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Franz S. Hover and Michael S. Triantafyllou (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform.