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Last updated:

September 23, 2023

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Description

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)

Course Curriculum

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

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