Advanced Probability Theory: 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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