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Probability and Statistics

Probability and Statistics. Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. The use of statistical reasoning and methodology is indispensable in modern world. It is true for any discipline, be it physical sciences, engineering and technology, economics or social sciences. Much of the advanced research in biology, genetics, and information science relies increasingly on use of statistical tools. It is essential for the students to get acquainted with the subject of probability and statistics at an early stage. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage. Each concept has been explained through examples and application oriented problems. (from nptel.ac.in)

Sets, Classes, Collections


Lecture 01 - Sets, Classes, Collections
Lecture 02 - Sequence of Sets
Lecture 03 - Rings and Fields, and their Properties
Lecture 04 - Sigma-Rings, Sigma-Fields, Monotone Classes
Lecture 05 - Random Experiments, Events
Lecture 06 - Definitions of Probability
Lecture 07 - Properties of Probability Function I: Addition Rule and Continuity
Lecture 08 - Properties of Probability Function II: Bonferroni and Boole's Inequalities
Lecture 09 - Conditional Probability
Lecture 10 - Independence of Events
Lecture 11 - Problems in Probability I
Lecture 12 - Problems in Probability II
Lecture 13 - Random Variables
Lecture 14 - Probability Distribution of a Random Variable I
Lecture 15 - Probability Distribution of a Random Variable II
Lecture 16 - Moments/ Mathematical Expectation
Lecture 17 - Characteristics of Distributions I
Lecture 18 - Characteristics of Distributions II
Lecture 19 - Special Discrete Distributions I
Lecture 20 - Special Discrete Distributions II
Lecture 21 - Special Discrete Distributions III
Lecture 22 - Poisson Process I
Lecture 23 - Poisson Process II
Lecture 24 - Special Continuous Distributions I
Lecture 25 - Special Continuous Distributions II
Lecture 26 - Special Continuous Distributions III
Lecture 27 - Special Continuous Distributions IV
Lecture 28 - Special Continuous Distributions V
Lecture 29 - Normal Distribution
Lecture 30 - Problems on Normal Distribution
Lecture 31 - Problems on Special Distributions I
Lecture 32 - Problems on Special Distributions II
Lecture 33 - Function of a Random Variable I
Lecture 34 - Function of a Random Variable II
Lecture 35 - Joint Distributions I
Lecture 36 - Joint Distributions II
Lecture 37 - Independence of Random Variables, Product Moments
Lecture 38 - Linearity Property of Correlation and Examples
Lecture 39 - Bivariate Normal Distribution I
Lecture 40 - Bivariate Normal Distribution II
Lecture 41 - Additive Properties of Distributions I
Lecture 42 - Additive Properties of Distributions II
Lecture 43 - Transformation of Random Variables
Lecture 44 - Distribution of Order Statistics
Lecture 45 - Basic Concepts of Sampling Distributions
Lecture 46 - Chi-Square Distribution
Lecture 47 - Chi-Square Distribution (cont.), t-Distribution
Lecture 48 - F-Distribution
Lecture 49 - Descriptive Statistics I
Lecture 50 - Descriptive Statistics II
Lecture 51 - Descriptive Statistics III
Lecture 52 - Descriptive Statistics IV
Lecture 53 - Introduction to Estimation
Lecture 54 - Unbiased and Consistent Estimators
Lecture 55 - Least Squares Estimation (LSE), Method of Moments Estimator (MME)
Lecture 56 - Examples on MME, Method of Maximum Likelihood Estimation (MLE)
Lecture 57 - Examples on MLE I
Lecture 58 - Examples on MLE II, Mean Square Error (MSE)
Lecture 59 - Uniformly Minimum-Variance Unbiased Estimator (UMVUE), Sufficiency, Completeness
Lecture 60 - Rao-Blackwell Theorem and its Applications
Lecture 61 - Confidence Intervals I
Lecture 62 - Confidence Intervals II
Lecture 63 - Confidence Intervals III
Lecture 64 - Confidence Intervals IV
Lecture 65 - Testing of Statistical Hypothesis: Basic Definitions
Lecture 66 - Type I and Type II Errors
Lecture 67 - Neyman-Pearson Fundamental Lemma
Lecture 68 - Applications of Neyman-Pearson Lemma I
Lecture 69 - Applications of Neyman-Pearson Lemma II
Lecture 70 - Testing for Normal Mean
Lecture 71 - Testing for Normal Variance
Lecture 72 - Large Sample Test for Variance and Two Sample Problem
Lecture 73 - Paired t-Test
Lecture 74 - Examples
Lecture 75 - Testing Equality of Proportions
Lecture 76 - Chi-Square Test for Goodness Fit I
Lecture 77 - Chi-Square Test for Goodness Fit II
Lecture 78 - Testing for Independence in rxc Contingency Table I
Lecture 79 - Testing for Independence in rxc Contingency Table II

References
Probability and Statistics
Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. The use of statistical reasoning and methodology is indispensable in modern world.