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Actuarial Fundamentals

4 articles

2026.03.05

Transforming a Random Variable Doesn't Move the Probability: The Inverse Function Trick

When an insurance policy modifies the payment based on the loss, what you have is a transformed random variable. Finding its percentiles doesn't require deriving a new distribution from scratch — it only requires inverting the transformation and using the CDF you already have.

transformationspercentilesexam-PSOAinsurance

Actuarial Fundamentals

2026.02.18

Why Insurance Works: The Central Limit Theorem and the Power of Aggregating Risk

Study guide for the third Exam P topic: multivariate variables, Eve's Law, and the CLT. The concepts that explain why insurance works as a business.

CLTexam-PSOAaggregationrisk

Actuarial Fundamentals

2026.02.18

Random Variables in Insurance: Deductibles, Limits, and the Math of Paying Claims

Study guide for the heaviest topic on Exam P: random variables, distributions, and payment modifications. The topic where mechanical errors hurt more than conceptual ones.

random-variablesexam-PSOAinsurancedistributions

Actuarial Fundamentals

2026.02.18

Actuarial Probability Foundations: What Exam P Reveals About Thinking in Risk

Study guide for the first section of the SOA Exam P: axioms, conditional probability, and Bayes. Not formulas to memorize, but the mental toolkit an actuary uses to classify risk and decide under uncertainty.

probabilityexam-PSOABayesrisk

Actuarial Fundamentals