STAT 202 · Year 2 · Semester 1 · 4 credits · Mathematics & Statistics

Mathematical Statistics

From sample data to optimal inference: master likelihood theory, efficiency bounds, and the mathematical engine of actuarial science.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

The Meridian Threshold

When a coastal reinsurance treaty threatens to trigger a forty-million-dollar solvency shortfall, a junior actuary must build an airtight inferential engine from first principles before the annual audit.

Protagonist · Maya Lin, an Associate Actuary at Meridian Re specializing in property-catastrophe reinsurance pricing.

Setting · Meridian Re's quantitative underwriting desk in Boston, facing scrutiny from state insurance commissioners ahead of annual treaty renewals.

Stakes · A forty-million-dollar capital reserve deficit will force a regulatory rating downgrade and trigger mandatory solvency liquidation if the tail risk and severity parameters are misjudged.

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Episodes

Season finale: Maya presents an exact order-statistic tail risk pricing model grounded in likelihood-ratio validated GLMs, resolving the solvency deficit and setting a new corporate standard for parameter risk governance.

From the lecturer: Welcome to STAT 202. This course transforms probability theory into the operational core of statistical decision-making, providing the rigorous grounding required for the SOA and CAS Mathematical Statistics VEE and serving as the mathematical bedrock for advanced predictive modeling exams like CAS MAS-I, MAS-II, and SOA ASTAM/ALTAM. To succeed, do not watch these films passively. Keep a clean derivation notebook, a dedicated standard distributions reference sheet, and a scientific calculator beside you. When an estimation problem or hypothesis test derivation begins, pause the video, write down the joint density or log-likelihood function yourself, and attempt the first-order conditions before watching the solution unfold. Pay special attention to the regularity conditions, the geometry of score functions, and the pivotal quantities underpinning confidence intervals. We will balance analytical derivations with intuitive geometric proofs and computational checks, ensuring you develop both the theoretical precision expected of a credentialed actuary and the practical intuition necessary to evaluate complex loss and claim models.

Cold open

At six in the morning, Maya stares at a spreadsheet flagged by the chief risk officer: thirty-two coastal flood claims from the past hurricane season, with a sample variance nearly triple the pricing team's baseline assumption. If the sample variance reflects true underlying volatility rather than random fluctuation, Meridian Re is undercapitalized by fifteen million dollars.

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Transcript

Define a random sample and characterize statistics as random variables with distinct sampling distributions.
Derive the exact distributions of the sample mean and sample variance under normal sampling using Cochran's theorem.
Construct Student's t and Snedecor's F statistics from first principles and identify their structural components.
Evaluate tail probabilities for sample statistics in property-casualty claim severity models.