List of Probability Topics - Random Variables

Random Variables

  • Discrete random variable
    • Probability mass function
  • Constant random variable
  • Expected value
    • Jensen's inequality
  • Variance
    • Standard deviation
    • Geometric standard deviation
  • Multivariate random variable
    • Joint probability distribution
    • Marginal distribution
    • Kirkwood approximation
  • Independent identically-distributed random variables
    • Independent and identically-distributed random variables
  • Statistical independence
    • Conditional independence
    • Pairwise independence
    • Covariance
    • Covariance matrix
    • De Finetti's theorem
  • Correlation
    • Uncorrelated
    • Correlation function
  • Canonical correlation
  • Convergence of random variables
    • Weak convergence of measures
      • Helly–Bray theorem
      • Slutsky's theorem
    • Skorokhod's representation theorem
    • Lévy's continuity theorem
    • Uniform integrability
  • Markov's inequality
  • Chebyshev's inequality = Chernoff bound
  • Chernoff's inequality
  • Bernstein inequalities (probability theory)
    • Hoeffding's inequality
  • Kolmogorov's inequality
  • Etemadi's inequality
  • Khintchine inequality
  • Paley–Zygmund inequality
  • Laws of large numbers
    • Asymptotic equipartition property
    • Typical set
    • Law of large numbers
  • Random field
    • Conditional random field
  • Borel-Cantelli lemma
  • Wick product

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