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

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Shalabh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104146)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104146)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 01: Data Science- Why, What, and How?](https://invisiblenetwork.ai/learn/nptel/111104146/31efad64c3ab) (Video)
2. [Lecture 02: Installation and Working with R](https://invisiblenetwork.ai/learn/nptel/111104146/fff4b29bb235) (Video)
3. [Lecture 03: Installation and Working with R Studio](https://invisiblenetwork.ai/learn/nptel/111104146/ef0f9b58b470) (Video)
4. [Lecture 04: Calculations with R as a Calculator](https://invisiblenetwork.ai/learn/nptel/111104146/a715532805d8) (Video)
5. [Lecture 05: Calculations with Data Vectors](https://invisiblenetwork.ai/learn/nptel/111104146/f306c1e38788) (Video)
6. [Lecture 06: Built-in Commands and Bivariate Plots](https://invisiblenetwork.ai/learn/nptel/111104146/2d9afd051724) (Video)
7. [Lecture 07: Logical Operators and Selection of Sample](https://invisiblenetwork.ai/learn/nptel/111104146/79ee37523b76) (Video)
8. [Lecture 8: Introduction to Probability](https://invisiblenetwork.ai/learn/nptel/111104146/62ad8098440e) (Video)
9. [Lecture 9: Sample Space and Events](https://invisiblenetwork.ai/learn/nptel/111104146/6b431a21e4f0) (Video)
10. [Lecture 10: Set Theory and Events using Venn Diagrams](https://invisiblenetwork.ai/learn/nptel/111104146/55f8b3accc38) (Video)
11. [Lecture 11: Relative Frequency and Probability](https://invisiblenetwork.ai/learn/nptel/111104146/409f40f90beb) (Video)
12. [Lecture 12: Probability and Relative Frequency - An Example](https://invisiblenetwork.ai/learn/nptel/111104146/bb0aaa513c48) (Video)
13. [Lecture 13: Axiomatic Definition of Probability](https://invisiblenetwork.ai/learn/nptel/111104146/a193d4058216) (Video)
14. [Lecture 14: Some Rules of Probability](https://invisiblenetwork.ai/learn/nptel/111104146/b8de0b128f86) (Video)
15. [Lecture 15: Basic Principles of Counting- Ordered Set, Unordered Set, and Permutations](https://invisiblenetwork.ai/learn/nptel/111104146/2ecff822f579) (Video)
16. [Lecture 16: Basic Principles of Counting- Combination](https://invisiblenetwork.ai/learn/nptel/111104146/865c9218ecc4) (Video)
17. [Lecture 17: Conditional Probability](https://invisiblenetwork.ai/learn/nptel/111104146/b92955504b01) (Video)
18. [Lecture 18: Multiplication Theorem of Probability](https://invisiblenetwork.ai/learn/nptel/111104146/a4cf5da53efc) (Video)
19. [Lecture 19: Bayes' Theorem](https://invisiblenetwork.ai/learn/nptel/111104146/9c3ce5cde23f) (Video)
20. [Lecture 20: Independent Events](https://invisiblenetwork.ai/learn/nptel/111104146/6bfc298f8900) (Video)
21. [Lecture 21: Computation of Probability using R](https://invisiblenetwork.ai/learn/nptel/111104146/b584acae30c8) (Video)
22. [Lecture 22: Random Variables - Discrete and Continuous](https://invisiblenetwork.ai/learn/nptel/111104146/e25ac3b9d24b) (Video)
23. [Lecture 23: Cumulative Distribution and Probability Density Function](https://invisiblenetwork.ai/learn/nptel/111104146/bd673e39a11d) (Video)
24. [Lecture 24: Discrete Random Variables, Probability Mass Function and Cumulative Distribution Function](https://invisiblenetwork.ai/learn/nptel/111104146/451187a0abe1) (Video)
25. [Lecture 25: Expectation of Variables](https://invisiblenetwork.ai/learn/nptel/111104146/73414a4b569e) (Video)
26. [Lecture 26: Moments and Variance](https://invisiblenetwork.ai/learn/nptel/111104146/51a5affae340) (Video)
27. [Lecture 27: Data Based Moments and Variance in R Software](https://invisiblenetwork.ai/learn/nptel/111104146/a486569481e8) (Video)
28. [Lecture 28: Skewness and Kurtosis](https://invisiblenetwork.ai/learn/nptel/111104146/4c635abf2b5a) (Video)
29. [Lecture 29: Quantiles and Tschebyschev's Inequality](https://invisiblenetwork.ai/learn/nptel/111104146/5387ae82222b) (Video)
30. [Lecture 30: Degenerate and Discrete Uniform Distributions](https://invisiblenetwork.ai/learn/nptel/111104146/094f2fc75a4d) (Video)
31. [Lecture 31: Discrete Uniform Distribution in R](https://invisiblenetwork.ai/learn/nptel/111104146/4077ac56f3fe) (Video)
32. [Lecture 32: Bernoulli and Binomial Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/1c069779c17e) (Video)
33. [Lecture 33: Binomial Distribution in R](https://invisiblenetwork.ai/learn/nptel/111104146/b4c6e734918e) (Video)
34. [Lecture 34: Poisson Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/c171d07a8bea) (Video)
35. [Lecture 35: Poisson Distribution in R](https://invisiblenetwork.ai/learn/nptel/111104146/6c35dec842f4) (Video)
36. [Lecture 36: Geometric Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/d31c06822ae3) (Video)
37. [Lecture 37: Geometric Distribution in R](https://invisiblenetwork.ai/learn/nptel/111104146/4f36c40f0e9f) (Video)
38. [Lecture 38: Continuous Random Variables and Uniform Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/872460cf0fb8) (Video)
39. [Lecture 39: Normal Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/7c1f61d1d215) (Video)
40. [Lecture 40: Normal Distribution in R](https://invisiblenetwork.ai/learn/nptel/111104146/31c14d0b144f) (Video)
41. [Lecture 41: Normal Distribution - More Results](https://invisiblenetwork.ai/learn/nptel/111104146/67b0ffd89b2d) (Video)
42. [Lecture 42: Exponential Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/10a94b2264a1) (Video)
43. [Lecture 43: Bivariate Probability Distribution for Discrete Random Variables](https://invisiblenetwork.ai/learn/nptel/111104146/f192283d57cf) (Video)
44. [Lecture 44: Bivariate Probability Distribution in R Software](https://invisiblenetwork.ai/learn/nptel/111104146/2fd7cba3302f) (Video)
45. [Lecture 45: Bivariate Probability Distribution for Continuous Random Variables](https://invisiblenetwork.ai/learn/nptel/111104146/6d0f20e53017) (Video)
46. [Lecture 46: Examples in Bivariate Probability Distribution Functions](https://invisiblenetwork.ai/learn/nptel/111104146/b582eaa728c2) (Video)
47. [Lecture 47: Covariance and Correlation](https://invisiblenetwork.ai/learn/nptel/111104146/d9454c78b2e2) (Video)
48. [Lecture 48: Covariance and Correlation - Examples and R Software](https://invisiblenetwork.ai/learn/nptel/111104146/1e33e31c9dbd) (Video)
49. [Lecture 49: Bivariate Normal Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/c777055e4ae0) (Video)
50. [Lecture 50: Chi square Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/73fad6573f25) (Video)
51. [Lecture 51: t - Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/084965c7e600) (Video)
52. [Lecture 52: F - Distribution](https://invisiblenetwork.ai/learn/nptel/111104146/2f9073ce9999) (Video)
53. [Lecture 53: Distribution of Sample Mean, Convergence in Probability and Weak Law of Large Numbers](https://invisiblenetwork.ai/learn/nptel/111104146/a260f07fcfa5) (Video)
54. [Lecture 54: Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/111104146/0827760535f3) (Video)
55. [Lecture 55: Needs for Drawing Statistical Inferences](https://invisiblenetwork.ai/learn/nptel/111104146/65ae4cc0363d) (Video)
56. [Lecture 56: Unbiased Estimators](https://invisiblenetwork.ai/learn/nptel/111104146/d7d4afefb3a5) (Video)
57. [Lecture 57: Efficiency of Estimators](https://invisiblenetwork.ai/learn/nptel/111104146/0d6980b05276) (Video)
58. [Lecture 58: Cramér-Rao Lower Bound and Efficiency of Estimators](https://invisiblenetwork.ai/learn/nptel/111104146/7b47bb85c8cb) (Video)
59. [Lecture 59: Consistency and Sufficiency of Estimators](https://invisiblenetwork.ai/learn/nptel/111104146/e8ab9d0b2da2) (Video)
60. [Lecture 60: Method of Moments](https://invisiblenetwork.ai/learn/nptel/111104146/38e57d7bf165) (Video)
61. [Lecture 61: Method of Maximum Likelihood and Rao Blackwell Theorem](https://invisiblenetwork.ai/learn/nptel/111104146/c6ff333dd5bf) (Video)
62. [Lecture 62: Basic Concepts of Confidence Interval Estimation](https://invisiblenetwork.ai/learn/nptel/111104146/c8e842eb8fb6) (Video)
63. [Lecture 63: Confidence Interval for Mean in One Sample with Known Variance](https://invisiblenetwork.ai/learn/nptel/111104146/bf14e0c51f77) (Video)
64. [Lecture 64: Confidence Interval for Mean and Variance](https://invisiblenetwork.ai/learn/nptel/111104146/96671352c864) (Video)
65. [Lecture 65: Basics of Tests of Hypothesis and Decision Rules](https://invisiblenetwork.ai/learn/nptel/111104146/c09876a6436e) (Video)
66. [Lecture 66: Test Procedures for One Sample Test for Mean with Known Variance](https://invisiblenetwork.ai/learn/nptel/111104146/798a9f876399) (Video)
67. [Lecture 67: One Sample Test for Mean with Unknown Variance](https://invisiblenetwork.ai/learn/nptel/111104146/1d1fd2831e45) (Video)
68. [Lecture 68: Two Sample Test for Mean with Known and Unknown Variances](https://invisiblenetwork.ai/learn/nptel/111104146/9caf6c80b917) (Video)
69. [Lecture 69: Test of Hypothesis for Variance in One and Two Samples](https://invisiblenetwork.ai/learn/nptel/111104146/78380221272e) (Video)
70. [Live Session 01-04-2021](https://invisiblenetwork.ai/learn/nptel/111104146/31efad64c3ab-2) (Video)
71. [Live Session 03-12-2022](https://invisiblenetwork.ai/learn/nptel/111104146/fff4b29bb235-2) (Video)
72. [Live Session 08-03-2024](https://invisiblenetwork.ai/learn/nptel/111104146/ef0f9b58b470-2) (Video)