Course Contents
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.
Course Synopsis
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.
Course Learning Outcomes
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.
Lecture 1: Probability Models and Axioms by John Tsitsiklis
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Element of and Cardinality of a set by Statistics with Anji
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Random experiment, Sample space and events by Statistics with Anji
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Statistical Inference(Casella), Lecture 1, Basics on Probability by Alan W
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Casella and Berger Statistical Inference Chapter 1 Problem 4 solution by Alan W
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Bayes rule by John Tsitsiklis
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Independence of Events by John Tsitsiklis
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Counting rules by John Tsitsiklis
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Discrete Random Variables; Probability Mass Functions; Expectations by John Tsitsiklis by
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Discrete Random Variable Examples; Joint PMFs by John Tsitsiklis
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conditional probability Lecture 2. Probability by Michael C. Cranston, Ph.D.
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Random Variables by Michael C. Cranston, Ph.D.
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Joint Distribution Michael C. Cranston, Ph.D.
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Expected Values by Michael C. Cranston, Ph.D.
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Multiple Discrete Random Variables: Expectations, Conditioning, Independence by John Tsitsiklis
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Continuous Random Variables by John Tsitsiklis
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Multiple Continuous Random Variables by John Tsitsiklis
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Continuous Bayes' Rule; Derived Distributions by John Tsitsiklis
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Derived Distributions; Covariance and Correlation by John Tsitsiklis
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Sum of a Random Number of Random Variables by John Tsitsiklis
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Introduction to Probability and Statistics 131A. Lecture 3. Random Variables by UCI Open
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Introduction to Probability and Statistics 131A. Lecture 5. Expected Values by UCI Open
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Moment Generating Function in Hindi [Lecture-25] by MA Classes
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Properties of Moment Generating Function in Hindi by MA Classes
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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