Probability Theory with Actuarial Applications 11CBSA8KJN

URI	`m2://res/11CBSA8KJN`
Kind	course
Creators	Neelesh S. Upadhye (instructor)
Date	2026-09-03
Scope	in
Ids	course 03v0r5n49:111106929

Expressions

e1: edition

Language	en
Date	2026-09-03

m1: page, IIT Madras (record). nptel 111106929
m2: page, 2026-09-03 (record). nptel 111106929

Contents

part 1: Week 1
session 1: W1_L1_The Language of Risk
session 2: W1_L2_The Art of Counting Combinatorics
session 3: W1_L3_Updating Beliefs Conditional Probability
session 4: W1_L4_Bayes' Theorem The Update Tool
session 5: W1_L5_Independence The Free Pass
part 2: Week 2
session 6: W2_L1_From Events to Numbers (Discrete RVs & PMF)
session 7: W2_L2_The Continuous World (Continuous RVs & PDF)
session 8: W2_L3_The "Grand Unifier'' (Cumulative Distribution Function)
session 9: W2_L4_The "Center of Gravity'' (Expected Value)
session 10: W2_L5_Functions of an RV (The Actuarial Toolkit)
part 3: Week 3
session 11: W3_L1_The "Yes/No'' World (Bernoulli & Binomial)
session 12: W3_L2_The "Claim Count'' Model (Poisson)
session 13: W3_L3_The "Waiting Time'' Model (Exponential)
session 14: W3_L4_The "Flexible'' Model (Gamma)
session 15: W3_L5_The "Everywhere" Model (Normal Distribution)
part 4: Week 4
session 16: W4_L1_Joint Distributions (Discrete PMF)
session 17: W4_L2_Joint Distributions (Continuous PDF)
session 18: W4_L3_Independence & Conditional Distributions
session 19: W4_L4_Covariance (Measuring Linear Relationship)
session 20: W4_L5_Correlation & Variance of Sums
part 5: Week 5
session 21: W5_L1_The "1D'' Transformation (The CDF Method)
session 22: W5_L2_The "1D'' Shortcut (Change of Variable)
session 23: W5_L3_The "2D'' Transformation (The Jacobian Method)
session 24: W5_L4_The "Aggregate Loss'' Transformation (Convolution)
session 25: W5_L5_The "Extreme Loss'' (Order Statistics)
part 6: Week 6
session 26: W6_L1_Conditional Expectation
session 27: W6_L2_The "Tower Property'' (Law of Total Expectation)
session 28: W6_L3_The Law of Total Variance (Eve's Law)
session 29: W6_L4_Conditioning Drills (Mixed Distributions)
session 30: W6_L5_Review (Compound vs. Mixed Models)
part 7: Week 7
session 31: W7_L1_The "Magic Tool'' (Moment-Generating Function)
session 32: W7_L2_The MGF "Lookup Table''
session 33: W7_L3_The "Payoff'' (MGF of Independent Sums)
session 34: W7_L4_Advanced Tools (CGFs & Compound Sum MGF)
session 35: W7_L5_Week 7 Review & Capstone Drill)
part 8: Week 8
session 36: W8_L1_The Problem of "Tails" (Why We Need Bounds)
session 37: W8_L2_The "Better'' Bound (Chebyshev's Inequality)
session 38: W8_L3_The Law of Large Numbers (LLN)
session 39: W8_L4_Other Inequalities (One-Sided Chebyshev & Jensen's)
session 40: W8_L5_Week 8 Review & Drills
part 9: Week 9
session 41: W9_L1_The Central Limit Theorem (CLT)
session 42: W9_L2_CLT Drills (Aggregate Loss Problems)
session 43: W9_L3_The Continuity Correction
session 44: W9_L4_Capstone Drill (CLT for Aggregate Losses)
session 45: W9_L5_The Approximation ``Decision Tree''
part 10: Week 10
session 46: W10_L1_The "Language'' of Insurance Models
session 47: W10_L2_Policy Feature 1 (Deductibles)
session 48: W10_L3_Policy Feature 2 (Policy Limits)
session 49: W10_L4_Capstone (Pricing a ``Policy Layer'')
session 50: W10_L5_Review & Introduction to Stop-Loss
part 11: Week 11
session 51: W11_L1_The "Master Formula" for Expected Aggregate Loss
session 52: W11_L2_The "Master Algorithm" for Var(S)
session 53: W11_L3_Finding Severity Moments E[Y^2] and Var(Y)
session 54: W11_L4_The "Master Algorithm'' Drill
session 55: W11_L5_Week 11 Review & Capstone Drills
part 12: Week 12
session 56: W12_L1_''The Big Picture'' Review (Part 1: The Toolkit)
session 57: W12_L2_''The Big Picture'' Review (Part 2: The Models)
session 58: W12_L3_Mock Exam Review (Part 1: Q1--10)
session 59: W12_L4_Mock Exam Review (Part 2: Q11--20)
session 60: W12_L5_Mock Exam Review (Part 3: Q21--30)

Catalogue records

nptel: 111106929 (manifestation)
nptel_video: 111106929 (manifestation)