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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)

Lecture 72 - Large Sample Test for Variance and Two Sample Problem

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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