4 articles
To find a percentile of a transformed random variable, such as an insurer's payment after a deductible, invert the transformation and use the CDF you already have instead of deriving a new distribution. The post builds this from the ordinary deductible, the way SOA Exam P tends to ask it.
The Central Limit Theorem (CLT) is the mathematical justification for why insurance works as a business: aggregating many risks makes the total behave predictably. This SOA Exam P study guide also covers multivariate random variables, covariance and dependence, and Eve's Law for decomposing variability.
The univariate random variables section, about 45% of SOA Exam P, tests distributions, expected values and payment modifications such as deductibles and limits, and mechanical errors cost more than conceptual ones. This study guide shows how the pieces connect and why they matter in insurance.
The first section of Exam P covers probability axioms, conditional probability and Bayes, the toolkit an actuary uses to classify risk and decide under uncertainty. This study guide explains why the SOA puts them first and how they connect to real actuarial work.