# Probability Foundations for Electrical Engineers

- Institution: IIT Madras
- Department: Electrical Engineering
- Taught by: Prof. Andrew Thangaraj, Prof. R. Aravind EE
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108106106)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108106106)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Experiments, Outcomes and Events](https://invisiblenetwork.ai/learn/nptel/108106106/c9123e6ca802) (Video)
2. [Examples: Experiments and sample spaces](https://invisiblenetwork.ai/learn/nptel/108106106/7482d34f3d70) (Video)
3. [Operations on Events](https://invisiblenetwork.ai/learn/nptel/108106106/21e89cda4ed9) (Video)
4. [Examples: Sample spaces and events](https://invisiblenetwork.ai/learn/nptel/108106106/252cf8ed94d4) (Video)
5. [Sigma Fields and Probability](https://invisiblenetwork.ai/learn/nptel/108106106/cd9e18828cd9) (Video)
6. [Discrete Sample Spaces](https://invisiblenetwork.ai/learn/nptel/108106106/d42a9e0cc537) (Video)
7. [Union and Partition](https://invisiblenetwork.ai/learn/nptel/108106106/b12e37710fe9) (Video)
8. [Examples: Probability Calculation for Equally likely Outcomes](https://invisiblenetwork.ai/learn/nptel/108106106/7c5c650bc571) (Video)
9. [Definition and Basic Properties](https://invisiblenetwork.ai/learn/nptel/108106106/0db17b0b2956) (Video)
10. [Bayes' Rule for Partitions](https://invisiblenetwork.ai/learn/nptel/108106106/a5b72ca6846e) (Video)
11. [Examples: Conditional probability](https://invisiblenetwork.ai/learn/nptel/108106106/1cda7472bd04) (Video)
12. [Example of Detection](https://invisiblenetwork.ai/learn/nptel/108106106/fc679221473d) (Video)
13. [Example: Coloured Cards from a Box](https://invisiblenetwork.ai/learn/nptel/108106106/1bda557aa3d0) (Video)
14. [Independence of Events](https://invisiblenetwork.ai/learn/nptel/108106106/b1e085e6108c) (Video)
15. [Examples: Independence](https://invisiblenetwork.ai/learn/nptel/108106106/f35f68aff187) (Video)
16. [Combining Independent Experiments](https://invisiblenetwork.ai/learn/nptel/108106106/371584aa7a71) (Video)
17. [Conditional Independence](https://invisiblenetwork.ai/learn/nptel/108106106/77b6698ab756) (Video)
18. [Examples and Computations with Conditional Independence](https://invisiblenetwork.ai/learn/nptel/108106106/b67f35b0d9d2) (Video)
19. [Binomial and Geometric Models](https://invisiblenetwork.ai/learn/nptel/108106106/04502e9e98ce) (Video)
20. [Examples: Binomial and Geometric Model](https://invisiblenetwork.ai/learn/nptel/108106106/aece0c623c03) (Video)
21. [Example: Random walk](https://invisiblenetwork.ai/learn/nptel/108106106/7b30e6151214) (Video)
22. [Definition and Discrete Setting](https://invisiblenetwork.ai/learn/nptel/108106106/6a1288055167) (Video)
23. [Random Variables and Events](https://invisiblenetwork.ai/learn/nptel/108106106/aa818285eb7a) (Video)
24. [Examples: Discrete random variables](https://invisiblenetwork.ai/learn/nptel/108106106/5dbcd2a7c45d) (Video)
25. [Important distributions](https://invisiblenetwork.ai/learn/nptel/108106106/15d805da32e6) (Video)
26. [Examples: Discrete PMFs](https://invisiblenetwork.ai/learn/nptel/108106106/25e8a56b4b6d) (Video)
27. [Real-life modeling example](https://invisiblenetwork.ai/learn/nptel/108106106/a7aaa7153547) (Video)
28. [More Distributions](https://invisiblenetwork.ai/learn/nptel/108106106/897f49eacfe8) (Video)
29. [Conditional PMFs, Conditioning on an event, Indicator random variables](https://invisiblenetwork.ai/learn/nptel/108106106/ba931f309ce0) (Video)
30. [Example: Conditioning on an event, Indicator random variables](https://invisiblenetwork.ai/learn/nptel/108106106/9f753563d9f1) (Video)
31. [Multiple random variables and joint distribution](https://invisiblenetwork.ai/learn/nptel/108106106/87c26cd47ddf) (Video)
32. [Example: Two random variables](https://invisiblenetwork.ai/learn/nptel/108106106/4971d5426786) (Video)
33. [Marginal PMF](https://invisiblenetwork.ai/learn/nptel/108106106/442a5b0b5b07) (Video)
34. [Trinomial joint PMF](https://invisiblenetwork.ai/learn/nptel/108106106/8504085329fd) (Video)
35. [Events and Conditioning with Two Random Variables](https://invisiblenetwork.ai/learn/nptel/108106106/7ed99cec1e08) (Video)
36. [Example: Compute Marginal and Conditional PMFs, Probability of Events](https://invisiblenetwork.ai/learn/nptel/108106106/c74a00c17862) (Video)
37. [Independent random variables](https://invisiblenetwork.ai/learn/nptel/108106106/988eef0a61e8) (Video)
38. [More on independence](https://invisiblenetwork.ai/learn/nptel/108106106/c8db77b92901) (Video)
39. [Example: IID Repetitions](https://invisiblenetwork.ai/learn/nptel/108106106/20b26d70063e) (Video)
40. [Addition of Random Variables](https://invisiblenetwork.ai/learn/nptel/108106106/edc56909a09a) (Video)
41. [Sum, Difference and Max of Two Random Variables](https://invisiblenetwork.ai/learn/nptel/108106106/97f399bb59d0) (Video)
42. [More Computations: Min of Two Random Variables](https://invisiblenetwork.ai/learn/nptel/108106106/d70e12da9925) (Video)
43. [Example: X+Y, X-Y, min(X,Y), max(X,Y)](https://invisiblenetwork.ai/learn/nptel/108106106/4774174cf1db) (Video)
44. [Real line as sample space](https://invisiblenetwork.ai/learn/nptel/108106106/0c57d283f818) (Video)
45. [Probability density function (pdf)](https://invisiblenetwork.ai/learn/nptel/108106106/0d67d198245b) (Video)
46. [Cumulative distribution function (CDF)](https://invisiblenetwork.ai/learn/nptel/108106106/ab0542df5844) (Video)
47. [Continuous random variables](https://invisiblenetwork.ai/learn/nptel/108106106/81e5c7811cd7) (Video)
48. [pdf and CDF of Continuous Random Variables](https://invisiblenetwork.ai/learn/nptel/108106106/a78737853960) (Video)
49. [Spinning pointer example](https://invisiblenetwork.ai/learn/nptel/108106106/8fb988f7498b) (Video)
50. [Important continuous distributions](https://invisiblenetwork.ai/learn/nptel/108106106/07f644ead9b1) (Video)
51. [More continuous distributions](https://invisiblenetwork.ai/learn/nptel/108106106/5cd576b167bd) (Video)
52. [Two-dimensional real sample space](https://invisiblenetwork.ai/learn/nptel/108106106/242a75fea7e4) (Video)
53. [Joint pdf and joint CDF](https://invisiblenetwork.ai/learn/nptel/108106106/7d4459dfdb54) (Video)
54. [More on assigning probability to regions of x-y plain](https://invisiblenetwork.ai/learn/nptel/108106106/596d1ca0182e) (Video)
55. [Darts example and marginal pdfs](https://invisiblenetwork.ai/learn/nptel/108106106/731124371715) (Video)
56. [Independence to two continuous random variables](https://invisiblenetwork.ai/learn/nptel/108106106/1674033d9222) (Video)
57. [Examples: two independent continuous random variables](https://invisiblenetwork.ai/learn/nptel/108106106/570c6fb8b05a) (Video)
58. [Prob X grater then Y : Computation of Probability of a Non-rectangular Region](https://invisiblenetwork.ai/learn/nptel/108106106/234d963e999d) (Video)
59. [Conditional pdfs for continuous r.v.](https://invisiblenetwork.ai/learn/nptel/108106106/335565c10795) (Video)
60. [Conditional pdfs (Continued)](https://invisiblenetwork.ai/learn/nptel/108106106/79343a605d09) (Video)
61. [Transformations of random variables](https://invisiblenetwork.ai/learn/nptel/108106106/ac8e0d3f2d56) (Video)
62. [CDF method](https://invisiblenetwork.ai/learn/nptel/108106106/3b5f9418a24c) (Video)
63. [pdf method](https://invisiblenetwork.ai/learn/nptel/108106106/a7a3df9f283a) (Video)
64. [Examples](https://invisiblenetwork.ai/learn/nptel/108106106/08694f9c18cd) (Video)
65. [One-to-one transformations](https://invisiblenetwork.ai/learn/nptel/108106106/c88df1d2fcbc) (Video)
66. [Expected Value or Mean of a Random Variable](https://invisiblenetwork.ai/learn/nptel/108106106/c227ea24b540) (Video)
67. [Properties of Expectation](https://invisiblenetwork.ai/learn/nptel/108106106/4301ffaf54aa) (Video)
68. [Examples: Symmetry](https://invisiblenetwork.ai/learn/nptel/108106106/4998dc8351c1) (Video)
69. [Expectation Computations for Important Distributions](https://invisiblenetwork.ai/learn/nptel/108106106/92fd55f5ce56) (Video)
70. [Variance](https://invisiblenetwork.ai/learn/nptel/108106106/4b73358d97d6) (Video)
71. [Examples of Variance](https://invisiblenetwork.ai/learn/nptel/108106106/5b728b278c92) (Video)
72. [Correlation and Covariance](https://invisiblenetwork.ai/learn/nptel/108106106/0aeab8620907) (Video)
73. [Expectations with two random variables](https://invisiblenetwork.ai/learn/nptel/108106106/1e31bf4211c0) (Video)
74. [Examples: Continuous Distributions](https://invisiblenetwork.ai/learn/nptel/108106106/8ab2085b282d) (Video)
75. [Examples: Discrete Distributions](https://invisiblenetwork.ai/learn/nptel/108106106/246b03e7630b) (Video)
76. [Covariance, continued](https://invisiblenetwork.ai/learn/nptel/108106106/f47912d9bcb8) (Video)
77. [Inequalities or Bounds involving E(.)](https://invisiblenetwork.ai/learn/nptel/108106106/6a4aff37aea3) (Video)
78. [Cauchy-Schwartz Inequality](https://invisiblenetwork.ai/learn/nptel/108106106/5a376fc6e0cd) (Video)
79. [Conditional Expectations](https://invisiblenetwork.ai/learn/nptel/108106106/d1c0f1c860ea) (Video)
80. [Eg of Conditional Expectations with Uniform r.v (in detail)](https://invisiblenetwork.ai/learn/nptel/108106106/c8b1ae41904b) (Video)
81. [Eg of Conditional Expectations with Poisson r.v (in detail)](https://invisiblenetwork.ai/learn/nptel/108106106/95c13e51b801) (Video)
82. [Weak Law of Large Numbers](https://invisiblenetwork.ai/learn/nptel/108106106/58e9740db8cf) (Video)
83. [Central Limit Theorem (with Examples)](https://invisiblenetwork.ai/learn/nptel/108106106/3f171f0e7037) (Video)