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Essentials of Data Science With R Software-1: Probability and Statistical Inference

Prof. Shalabh · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 01: Data Science- Why, What, and How? Video
  2. Lecture 02: Installation and Working with R Video
  3. Lecture 03: Installation and Working with R Studio Video
  4. Lecture 04: Calculations with R as a Calculator Video
  5. Lecture 05: Calculations with Data Vectors Video
  6. Lecture 06: Built-in Commands and Bivariate Plots Video
  7. Lecture 07: Logical Operators and Selection of Sample Video

Week 2

  1. Lecture 8: Introduction to Probability Video
  2. Lecture 9: Sample Space and Events Video
  3. Lecture 10: Set Theory and Events using Venn Diagrams Video
  4. Lecture 11: Relative Frequency and Probability Video
  5. Lecture 12: Probability and Relative Frequency - An Example Video
  6. Lecture 13: Axiomatic Definition of Probability Video

Week 3

  1. Lecture 14: Some Rules of Probability Video
  2. Lecture 15: Basic Principles of Counting- Ordered Set, Unordered Set, and Permutations Video
  3. Lecture 16: Basic Principles of Counting- Combination Video
  4. Lecture 17: Conditional Probability Video
  5. Lecture 18: Multiplication Theorem of Probability Video
  6. Lecture 19: Bayes' Theorem Video

Week 4

  1. Lecture 20: Independent Events Video
  2. Lecture 21: Computation of Probability using R Video
  3. Lecture 22: Random Variables - Discrete and Continuous Video
  4. Lecture 23: Cumulative Distribution and Probability Density Function Video
  5. Lecture 24: Discrete Random Variables, Probability Mass Function and Cumulative Distribution Function Video
  6. Lecture 25: Expectation of Variables Video

Week 5

  1. Lecture 26: Moments and Variance Video
  2. Lecture 27: Data Based Moments and Variance in R Software Video
  3. Lecture 28: Skewness and Kurtosis Video
  4. Lecture 29: Quantiles and Tschebyschev's Inequality Video
  5. Lecture 30: Degenerate and Discrete Uniform Distributions Video
  6. Lecture 31: Discrete Uniform Distribution in R Video

Week 6

  1. Lecture 32: Bernoulli and Binomial Distribution Video
  2. Lecture 33: Binomial Distribution in R Video
  3. Lecture 34: Poisson Distribution Video
  4. Lecture 35: Poisson Distribution in R Video
  5. Lecture 36: Geometric Distribution Video
  6. Lecture 37: Geometric Distribution in R Video

Week 7

  1. Lecture 38: Continuous Random Variables and Uniform Distribution Video
  2. Lecture 39: Normal Distribution Video
  3. Lecture 40: Normal Distribution in R Video
  4. Lecture 41: Normal Distribution - More Results Video
  5. Lecture 42: Exponential Distribution Video

Week 8

  1. Lecture 43: Bivariate Probability Distribution for Discrete Random Variables Video
  2. Lecture 44: Bivariate Probability Distribution in R Software Video
  3. Lecture 45: Bivariate Probability Distribution for Continuous Random Variables Video
  4. Lecture 46: Examples in Bivariate Probability Distribution Functions Video
  5. Lecture 47: Covariance and Correlation Video
  6. Lecture 48: Covariance and Correlation - Examples and R Software Video

Week 9

  1. Lecture 49: Bivariate Normal Distribution Video
  2. Lecture 50: Chi square Distribution Video
  3. Lecture 51: t - Distribution Video
  4. Lecture 52: F - Distribution Video
  5. Lecture 53: Distribution of Sample Mean, Convergence in Probability and Weak Law of Large Numbers Video

Week 10

  1. Lecture 54: Central Limit Theorem Video
  2. Lecture 55: Needs for Drawing Statistical Inferences Video
  3. Lecture 56: Unbiased Estimators Video
  4. Lecture 57: Efficiency of Estimators Video
  5. Lecture 58: Cramér-Rao Lower Bound and Efficiency of Estimators Video

Week 11

  1. Lecture 59: Consistency and Sufficiency of Estimators Video
  2. Lecture 60: Method of Moments Video
  3. Lecture 61: Method of Maximum Likelihood and Rao Blackwell Theorem Video
  4. Lecture 62: Basic Concepts of Confidence Interval Estimation Video
  5. Lecture 63: Confidence Interval for Mean in One Sample with Known Variance Video
  6. Lecture 64: Confidence Interval for Mean and Variance Video

Week 12

  1. Lecture 65: Basics of Tests of Hypothesis and Decision Rules Video
  2. Lecture 66: Test Procedures for One Sample Test for Mean with Known Variance Video
  3. Lecture 67: One Sample Test for Mean with Unknown Variance Video
  4. Lecture 68: Two Sample Test for Mean with Known and Unknown Variances Video
  5. Lecture 69: Test of Hypothesis for Variance in One and Two Samples Video

Live Session

  1. Live Session 01-04-2021 Video
  2. Live Session 03-12-2022 Video
  3. Live Session 08-03-2024 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Shalabh
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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