Random Variable, Probability Space, Borel set, Distribution function, Functions of Random Variable, Generating Functions, Characteristic function, Uniqueness theorem, Moment inequalities, Random vectors and multivariable continuous & discrete distributions. Functions of random vectors, Order Statistics. Special continuous and discrete distributions. Exponential family of distributions. Limit theorems, Sample moments and their distributions, systems of distribution: Pearson and Johnson.

To understand the concepts about the characteristics and properties of different discrete, continuous and exponential family of distributions in a broader dimension equipped with the mathematical and statistical skills.

Students will be expected to have: Knowledge in using mathematical tools to derive and describe the properties of different types of random variables and their distributions. Advanced concepts in the mathematical statistics with the capacity for problem-solving at a higher level. Understanding to use these skills to conduct research in field of mathematical statistics and to translate real-world problems into probability models.

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Book Title : Statistical Inference

Author : George Casella & Roger L.Berger

Edition : 2nd edition

Publisher : Duxburry Advanced Series

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Book Title : An introduction to probability and statistics

Author : Vijay K.Rohatgi & A.K Md. Ehsanes Saleh

Edition : 2nd edition

Publisher : Wiley Series

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Title : Book : Statistical Inference

Type : Curriculum Book

View Book : Statistical Inference