ECEN 303

Examination Probability and Random Variables

  1.  Discrete Probability
    •  Joint/Conditional probabilities
    •  Independence
    •  Bayes’ theorem
    •  Discrete random variables
  2.  Continuous Random Variables
    •  Cumulative distribution functions (CDFs) and probability density functions (PDFs)
    •  Gaussian random variables, standardized Gaussian integrals
    •  Conditional distribution and density functions
    •  Expected values, moments and conditional expected values
    •  Transformations of random variables
    •  Characteristic functions and moment generating functions
    •  Chernoff Bounds
  3.  Multiple random variables
    •  Joint and conditional CDFs and PDFs
    •  Independence
    •  Jointly Gaussian random variables
    •  Transformations of multiple random variables
    •  Random sequences – definitions of convergence modes and relationships between various modes
    •  Law of large numbers
    •  Central limit theorem