Advanced Probability Theory: Course Outline
- Probability review.
- Conditional Expectation.
- Theorems of total expectation and total variance with proofs and application.
- Transformation of random variables.
- 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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