# Probability Theory with Actuarial Applications

- Institution: IIT Madras
- Department: Mathematics
- Teacher: Prof. Neelesh S. Upadhye
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106929)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106929)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [W1_L1_The Language of Risk](https://invisiblenetwork.ai/learn/nptel/111106929/2aefa63f9125) (Video)
2. [W1_L2_The Art of Counting Combinatorics](https://invisiblenetwork.ai/learn/nptel/111106929/7d82514bbf15) (Video)
3. [W1_L3_Updating Beliefs Conditional Probability](https://invisiblenetwork.ai/learn/nptel/111106929/823fc0f52efe) (Video)
4. [W1_L4_Bayes' Theorem The Update Tool](https://invisiblenetwork.ai/learn/nptel/111106929/91acf12b27db) (Video)
5. [W1_L5_Independence The Free Pass](https://invisiblenetwork.ai/learn/nptel/111106929/65e352c9cdb8) (Video)
6. [W2_L1_From Events to Numbers (Discrete RVs & PMF)](https://invisiblenetwork.ai/learn/nptel/111106929/d0eafa508820) (Video)
7. [W2_L2_The Continuous World (Continuous RVs & PDF)](https://invisiblenetwork.ai/learn/nptel/111106929/dbccc22efb88) (Video)
8. [W2_L3_The "Grand Unifier'' (Cumulative Distribution Function)](https://invisiblenetwork.ai/learn/nptel/111106929/176275c5876b) (Video)
9. [W2_L4_The "Center of Gravity'' (Expected Value)](https://invisiblenetwork.ai/learn/nptel/111106929/ad2edfaf62bd) (Video)
10. [W2_L5_Functions of an RV (The Actuarial Toolkit)](https://invisiblenetwork.ai/learn/nptel/111106929/cd21696a852e) (Video)
11. [W3_L1_The "Yes/No'' World (Bernoulli & Binomial)](https://invisiblenetwork.ai/learn/nptel/111106929/5a76e1d2a5ea) (Video)
12. [W3_L2_The "Claim Count'' Model (Poisson)](https://invisiblenetwork.ai/learn/nptel/111106929/63b62e072900) (Video)
13. [W3_L3_The "Waiting Time'' Model (Exponential)](https://invisiblenetwork.ai/learn/nptel/111106929/f1593ca86a9f) (Video)
14. [W3_L4_The "Flexible'' Model (Gamma)](https://invisiblenetwork.ai/learn/nptel/111106929/9df43642a83f) (Video)
15. [W3_L5_The "Everywhere" Model (Normal Distribution)](https://invisiblenetwork.ai/learn/nptel/111106929/cf43dbd2b66c) (Video)
16. [W4_L1_Joint Distributions (Discrete PMF)](https://invisiblenetwork.ai/learn/nptel/111106929/0ebbf1921f3f) (Video)
17. [W4_L2_Joint Distributions (Continuous PDF)](https://invisiblenetwork.ai/learn/nptel/111106929/05e03f9850a2) (Video)
18. [W4_L3_Independence & Conditional Distributions](https://invisiblenetwork.ai/learn/nptel/111106929/edf59fb25591) (Video)
19. [W4_L4_Covariance (Measuring Linear Relationship)](https://invisiblenetwork.ai/learn/nptel/111106929/588d769e8dfe) (Video)
20. [W4_L5_Correlation & Variance of Sums](https://invisiblenetwork.ai/learn/nptel/111106929/5de22b3b4d04) (Video)
21. [W5_L1_The "1D'' Transformation (The CDF Method)](https://invisiblenetwork.ai/learn/nptel/111106929/d827cf18fc1e) (Video)
22. [W5_L2_The "1D'' Shortcut (Change of Variable)](https://invisiblenetwork.ai/learn/nptel/111106929/706c8d21d0da) (Video)
23. [W5_L3_The "2D'' Transformation (The Jacobian Method)](https://invisiblenetwork.ai/learn/nptel/111106929/7b813ba8db60) (Video)
24. [W5_L4_The "Aggregate Loss'' Transformation (Convolution)](https://invisiblenetwork.ai/learn/nptel/111106929/e07d4024776e) (Video)
25. [W5_L5_The "Extreme Loss'' (Order Statistics)](https://invisiblenetwork.ai/learn/nptel/111106929/092a8c7690e7) (Video)
26. [W6_L1_Conditional Expectation](https://invisiblenetwork.ai/learn/nptel/111106929/dd47206fb8b4) (Video)
27. [W6_L2_The "Tower Property'' (Law of Total Expectation)](https://invisiblenetwork.ai/learn/nptel/111106929/f45575929d44) (Video)
28. [W6_L3_The Law of Total Variance (Eve's Law)](https://invisiblenetwork.ai/learn/nptel/111106929/93e8727e38b9) (Video)
29. [W6_L4_Conditioning Drills (Mixed Distributions)](https://invisiblenetwork.ai/learn/nptel/111106929/39794b58f0c1) (Video)
30. [W6_L5_Review (Compound vs. Mixed Models)](https://invisiblenetwork.ai/learn/nptel/111106929/09edb1407ab0) (Video)
31. [W7_L1_The "Magic Tool'' (Moment-Generating Function)](https://invisiblenetwork.ai/learn/nptel/111106929/7cb60af8cb6d) (Video)
32. [W7_L2_The MGF "Lookup Table''](https://invisiblenetwork.ai/learn/nptel/111106929/b7b1e548515f) (Video)
33. [W7_L3_The "Payoff'' (MGF of Independent Sums)](https://invisiblenetwork.ai/learn/nptel/111106929/4a164a2ca5a8) (Video)
34. [W7_L4_Advanced Tools (CGFs & Compound Sum MGF)](https://invisiblenetwork.ai/learn/nptel/111106929/5fb9200702da) (Video)
35. [W7_L5_Week 7 Review & Capstone Drill)](https://invisiblenetwork.ai/learn/nptel/111106929/77e3042b6822) (Video)
36. [W8_L1_The Problem of "Tails" (Why We Need Bounds)](https://invisiblenetwork.ai/learn/nptel/111106929/b7a01f103e35) (Video)
37. [W8_L2_The "Better'' Bound (Chebyshev's Inequality)](https://invisiblenetwork.ai/learn/nptel/111106929/c27fee64b845) (Video)
38. [W8_L3_The Law of Large Numbers (LLN)](https://invisiblenetwork.ai/learn/nptel/111106929/cd6e38028c05) (Video)
39. [W8_L4_Other Inequalities (One-Sided Chebyshev & Jensen's)](https://invisiblenetwork.ai/learn/nptel/111106929/55d2b91b3927) (Video)
40. [W8_L5_Week 8 Review & Drills](https://invisiblenetwork.ai/learn/nptel/111106929/450296897e4e) (Video)
41. [W9_L1_The Central Limit Theorem (CLT)](https://invisiblenetwork.ai/learn/nptel/111106929/9692b288fb22) (Video)
42. [W9_L2_CLT Drills (Aggregate Loss Problems)](https://invisiblenetwork.ai/learn/nptel/111106929/2bb7f721ee0c) (Video)
43. [W9_L3_The Continuity Correction](https://invisiblenetwork.ai/learn/nptel/111106929/44ba26ee7de2) (Video)
44. [W9_L4_Capstone Drill (CLT for Aggregate Losses)](https://invisiblenetwork.ai/learn/nptel/111106929/5300a7bf563a) (Video)
45. [W9_L5_The Approximation ``Decision Tree''](https://invisiblenetwork.ai/learn/nptel/111106929/a120eada1b63) (Video)
46. [W10_L1_The "Language'' of Insurance Models](https://invisiblenetwork.ai/learn/nptel/111106929/3228e646c18f) (Video)
47. [W10_L2_Policy Feature 1 (Deductibles)](https://invisiblenetwork.ai/learn/nptel/111106929/34a393cd7a29) (Video)
48. [W10_L3_Policy Feature 2 (Policy Limits)](https://invisiblenetwork.ai/learn/nptel/111106929/16fc4ad518f3) (Video)
49. [W10_L4_Capstone (Pricing a ``Policy Layer'')](https://invisiblenetwork.ai/learn/nptel/111106929/f43beac5d76f) (Video)
50. [W10_L5_Review & Introduction to Stop-Loss](https://invisiblenetwork.ai/learn/nptel/111106929/963f5e8656a3) (Video)
51. [W11_L1_The "Master Formula" for Expected Aggregate Loss](https://invisiblenetwork.ai/learn/nptel/111106929/8b5e97b86efe) (Video)
52. [W11_L2_The "Master Algorithm" for Var(S)](https://invisiblenetwork.ai/learn/nptel/111106929/596315e89b6c) (Video)
53. [W11_L3_Finding Severity Moments E\[Y^2\] and Var(Y)](https://invisiblenetwork.ai/learn/nptel/111106929/2b36a778410c) (Video)
54. [W11_L4_The "Master Algorithm'' Drill](https://invisiblenetwork.ai/learn/nptel/111106929/b2d589a2cd62) (Video)
55. [W11_L5_Week 11 Review & Capstone Drills](https://invisiblenetwork.ai/learn/nptel/111106929/5a551acba4b6) (Video)
56. [W12_L1_''The Big Picture'' Review (Part 1: The Toolkit)](https://invisiblenetwork.ai/learn/nptel/111106929/ee88fde1e8b1) (Video)
57. [W12_L2_''The Big Picture'' Review (Part 2: The Models)](https://invisiblenetwork.ai/learn/nptel/111106929/ba0e23a381f2) (Video)
58. [W12_L3_Mock Exam Review (Part 1: Q1--10)](https://invisiblenetwork.ai/learn/nptel/111106929/21b326438316) (Video)
59. [W12_L4_Mock Exam Review (Part 2: Q11--20)](https://invisiblenetwork.ai/learn/nptel/111106929/9fefba4db148) (Video)
60. [W12_L5_Mock Exam Review (Part 3: Q21--30)](https://invisiblenetwork.ai/learn/nptel/111106929/bd1572d73e04) (Video)