MAS-I study plan

Compute conditional probabilities and apply Bayes' theorem to multi-stage risk scenarios without consulting notes.

Derive the mean, variance, and moment-generating function for the standard discrete and continuous families, then match each family to a written scenario description.

Solve combinatorial counting problems (permutations, combinations, occupancy) and state which counting rule applies and why.

Estimate parameters by method of moments and by maximum likelihood from raw samples, showing every algebraic step.

Construct confidence intervals and run one-sample and two-sample hypothesis tests, stating distributional assumptions explicitly for each.

Apply the central limit theorem and normal approximation to justify sampling-distribution choices in written solutions.

Compute present and accumulated values under simple and compound interest, including fractional time periods and unknown-rate solves.

Solve annuity-immediate, annuity-due, and varying payment stream problems, converting between timing conventions without formula lookup.

Value coupon bonds, compute yield to maturity, and build a period-by-period premium or discount amortization schedule.

Compute Macaulay and modified duration and convexity, and construct a two-asset immunization of a stated liability stream.

Translate between spot, forward, and yield-curve representations and price cash flows off each representation consistently.

Solve net present value and internal rate of return problems, including at least two cases where the IRR is non-unique or undefined and explain the correct decision rule.

Complete full derivations of mixed probability and interest-theory problems under a strict per-question time cap.

Combine frequency and severity distributions into aggregate loss models and compute the mean, variance, and selected quantiles of aggregate claims.

Apply limited expected value and stop-loss transform concepts to compute layer costs for stated retentions and limits.

Construct survival and hazard functions from a stated distribution and compute present values of life-contingent payments under each.

Apply limited-fluctuation and Bühlmann credibility to blend manual and observed experience, showing the credibility factor derivation.

Explain the surplus process and adjustment coefficient as tools for assessing ruin probability, and compute a ruin-related quantity for a small portfolio.

Explain the roles of state vs. federal regulation, model-law adoption, rate filing, and solvency monitoring in the U.S. insurance market.

Classify given insurance products by line of business and identify which regulatory requirements and risk-transfer mechanisms apply to each.

Recall and apply the core insurance doctrines (indemnity, insurable interest, utmost good faith, subrogation, proximate cause) to resolve at least 20 written claim scenarios.

Explain the regulatory rationale behind capital requirements and reserve standards and predict which rule governs a described situation.

Re-drill all previously logged financial-mathematics errors until each is solved correctly without notes on two consecutive attempts.

Complete three full-length timed practice exams under exam-day conditions, including a single-sitting run of at least four hours.

Diagnose weak sub-topics from each score report and re-solve every missed item to a complete derivation before the next attempt.

Consolidate four one-page domain summary sheets from the error journal and verify each key formula by reproducing it from memory.