# Probability Theory for Data Science - Institution: IIT Tirupati - Department: Mathematics - Teacher: Prof. Ishapathik Das - Level: Undergraduate - Language: English - Subjects: Mathematics - Source: [NPTEL](https://nptel.ac.in/courses/111106525) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/111106525) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) "Probability Theory for Data Science" is a specialized course designed to equip students with the essential knowledge and skills needed to analyze uncertain phenomena and make data-driven decisions in various domains. It provides a comprehensive understanding of the principles of probability and their applications in the context of data science. This course is essential for anyone aspiring to work in data-driven fields such as machine learning, artificial intelligence, statistics, and predictive analytics. The course typically begins with an introduction to basic concepts in probability theory, including sample spaces, events, and different approaches to defining probability. Emphasis is placed on developing a solid grasp of fundamental probability rules, such as the addition and multiplication rules, as well as understanding conditional probability, independence, and Bayes theorem. As the course progresses, students delve deeper into more advanced topics, such as random variables, probability distributions, and expectation. They explore common probability distributions, including binomial, Poisson, uniform, exponential, and normal distributions, and they learn how to calculate probabilities and expected values associated with these distributions. Additionally, students gain insight into concepts like moments, variance, and covariance, which are crucial for understanding data variability in real-world scenarios. Following this, students delve into the study of multiple random variables, exploring concepts such as the transformation of random variables, moment-generating functions, and key theorems pertaining to the convergence of random variables. "Probability Theory for Data Science" equips students with a strong theoretical foundation in probability and the analytical skills necessary to tackle complex data-driven problems. By mastering the principles of probability theory and its applications in data science, students are better prepared to excel in diverse… ## Lectures 1. [Introduction](https://invisiblenetwork.ai/learn/nptel/111106525/c9180a7d4116) (YouTube) 2. [Sample Space and Events](https://invisiblenetwork.ai/learn/nptel/111106525/8e4f429a0f1f) (YouTube) 3. [Special Events and Various Approaches to Defining Probability](https://invisiblenetwork.ai/learn/nptel/111106525/8a5550e693f6) (YouTube) 4. [Important Theorems](https://invisiblenetwork.ai/learn/nptel/111106525/a796a38c0881) (YouTube) 5. [Numerical Examples and Introduction to Conditional Probability](https://invisiblenetwork.ai/learn/nptel/111106525/dd3e2df353df) (YouTube) 6. [Definition of Conditional Probability and Independence](https://invisiblenetwork.ai/learn/nptel/111106525/44247ee285d1) (YouTube) 7. [Bayes' Theorem](https://invisiblenetwork.ai/learn/nptel/111106525/9185ab9c7568) (YouTube) 8. [Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/854bad105bc7) (YouTube) 9. [Events Defined by a Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/8d7309054ab6) (YouTube) 10. [Cumulative Distribution Function](https://invisiblenetwork.ai/learn/nptel/111106525/09f7eb4ec830) (YouTube) 11. [Properties of the Cumulative Distribution Function and Discrete Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/3abef50b1292) (YouTube) 12. [Probability Mass Function](https://invisiblenetwork.ai/learn/nptel/111106525/7e86e27ad2c0) (YouTube) 13. [Continuous Random Variable and Probability Density Function](https://invisiblenetwork.ai/learn/nptel/111106525/7bce65eb10ae) (YouTube) 14. [Numerical Examples](https://invisiblenetwork.ai/learn/nptel/111106525/b736b8178b9e) (YouTube) 15. [Moments](https://invisiblenetwork.ai/learn/nptel/111106525/8b65434d1099) (YouTube) 16. [Higher Order Moments and Variance of a Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/be16f2d9992c) (YouTube) 17. [Numerical Examples of Moments and Bernoulli Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/d1ecdd884574) (YouTube) 18. [Binomial Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/6980ffe22cf4) (YouTube) 19. [Applications of Binomial Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/d8d4d2417139) (YouTube) 20. [Poisson Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/fbc96697b1a8) (YouTube) 21. [Applications of Poisson Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/f4bb3b6d3e6b) (YouTube) 22. [Numerical Examples of Poisson Distribution and Uniform Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/ea14830b913e) (YouTube) 23. [Application of Uniform Distribution and Exponential Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/5e732cd9dec4) (YouTube) 24. [Applications of Exponential Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/fd1efd9396b0) (YouTube) 25. [Memoryless Property and Gamma Distributio](https://invisiblenetwork.ai/learn/nptel/111106525/4144728703c2) (YouTube) 26. [Example of Gamma Distribution and Normal Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/5ad89bd84b97) (YouTube) 27. [Properties of Normal Distributions](https://invisiblenetwork.ai/learn/nptel/111106525/9d288bf80902) (YouTube) 28. [Numerical Examples of Normal Distributions](https://invisiblenetwork.ai/learn/nptel/111106525/b4ab7a63b6a5) (YouTube) 29. [Applications of Normal Distributions and Conditional Distribution Function](https://invisiblenetwork.ai/learn/nptel/111106525/631d27590fb9) (YouTube) 30. [Examples of Conditional Distribution Function and Bivariate Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/c6d9434174ae) (YouTube) 31. [Example of Bivariate Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/f82e0f1feac6) (YouTube) 32. [Properties of the Joint Cumulative Distribution Function of a Bivariate Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/30d63104780b) (YouTube) 33. [Independence Between Two Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/f41da3319b34) (YouTube) 34. [Examples of Joint Cumulative Distribution Functions, Marginals, and Independence](https://invisiblenetwork.ai/learn/nptel/111106525/6a7826e97133) (YouTube) 35. [Joint Probability Mass Function, Marginal Probability Mass Function, Examples](https://invisiblenetwork.ai/learn/nptel/111106525/af16593e45e8) (YouTube) 36. [Numerical Examples on Bivariate Discrete Random Variables and the Concept of Joint Probability Density Function](https://invisiblenetwork.ai/learn/nptel/111106525/53f544eed4c5) (YouTube) 37. [Marginal Probability Density Function, Independence, and Examples](https://invisiblenetwork.ai/learn/nptel/111106525/c463a16f127f) (YouTube) 38. [Numerical Examples on Probability Density Function](https://invisiblenetwork.ai/learn/nptel/111106525/828a98ab97c4) (YouTube) 39. [Conditional Probability Mass Function](https://invisiblenetwork.ai/learn/nptel/111106525/52193133a594) (YouTube) 40. [Conditional Probability Density Function](https://invisiblenetwork.ai/learn/nptel/111106525/91eec621e545) (YouTube) 41. [Moments for Bivariate Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/a24cd4552ede) (YouTube) 42. [Association Between Two Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/dd7bc593939b) (YouTube) 43. [Numerical Examples on Moments for Bivariate Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/a5a1ed916769) (YouTube) 44. [Conditional Mean and Variance for Discrete Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/9b2830fba1be) (YouTube) 45. [Conditional Mean and Variance for Continuous Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/3b90a56f6a58) (YouTube) 46. [Numerical Examples on Conditional Mean and Variance](https://invisiblenetwork.ai/learn/nptel/111106525/086c978b9546) (YouTube) 47. [Multivariate Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/4d880d1ec315) (YouTube) 48. [Multivariate Probability Density Function and Independence](https://invisiblenetwork.ai/learn/nptel/111106525/c8e72e163774) (YouTube) 49. [Moments of a Multivariate Random Variable](https://invisiblenetwork.ai/learn/nptel/111106525/89a191fc8ac8) (YouTube) 50. [Numerical Examples on Joint Probability Mass Functions](https://invisiblenetwork.ai/learn/nptel/111106525/024e6e6c6280) (YouTube) 51. [Numerical Examples on Joint Probability Density Functions](https://invisiblenetwork.ai/learn/nptel/111106525/5a2aadb68f07) (YouTube) 52. [Multinomial Distribution and Multivariate Normal Distribution](https://invisiblenetwork.ai/learn/nptel/111106525/86b48ba2e725) (YouTube) 53. [Transformation of Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/9346c2286580) (YouTube) 54. [Theorem on Transformation of Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/f6790d6323b8) (YouTube) 55. [Transformation of Multivariate Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/1b2d8cc6f45e) (YouTube) 56. [Examples of Transformation of Bivariate Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/c3661be60938) (YouTube) 57. [Convolution and Example on Transformation of n-variate Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/0322b1274cc4) (YouTube) 58. [Transformation of Discrete Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/aa85acf3bd6f) (YouTube) 59. [Moment Generating Functions](https://invisiblenetwork.ai/learn/nptel/111106525/de7e9aa0a151) (YouTube) 60. [Example of Moment Generating Functions](https://invisiblenetwork.ai/learn/nptel/111106525/fda200dba4e4) (YouTube) 61. [Moment Generating Functions for the Transformation of Random Variables](https://invisiblenetwork.ai/learn/nptel/111106525/4bda7f81f150) (YouTube) 62. [Chebyshev's Inequality](https://invisiblenetwork.ai/learn/nptel/111106525/259d7ccf72bb) (YouTube) 63. [Notions of Convergence, Law of Large Numbers, and the Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/111106525/55aa8079045e) (YouTube)