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Advanced Probability Theory: Course Outline

Course Outline

  • Probability review.
  • Conditional Expectation.
  • Theorems of total expectation and total variance with proofs and application.
  • Transformation of random variables.
  • Change-of-variable.
  • Moment generating function and Distribution function techniques.
  • Order statistic and the sampling distributions of the smallest the largest, k’th order statistics.
  • Range, midrange, median, and pair of i’th and j’th order statistics.
  • Characteristic function. 
  • Inversion theorems for continuous and discrete random variables with proofs and application.
  • Non-central Chi-square, t and F distributions with application and properties.
  • Pearsonian system of distributions,
  • Sampling distribution of extreme values.  

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