A review of random variables


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  • The following topics will be covered in this lecture:
    • Basic set theory
    • Probabilistic experiments with finite outcome spaces
    • Basic probability
    • Discrete random variables
    • Continuous random variables
    • Parameters of probability distributions

Basic set theory: a history of sets

  • In the nineteenth century, the Georg Cantor developed the greater part of modern set theory.
  • Set theory is at the basis of mathematical logic and how mathematical objects are ordered in hierarchies of classes with certain properties.
  • At the turn of the nineteenth and twentieth centuries, Ernst Zermelo, Bertrand Russell, Cesare Burali-Forti and others found contradictions in the originally proposed set theory, with one of the famous results being Russell’s paradox.