IAI CS1 study plan

IAI CS1 · Give each week a clear focus.

8 weeks · About 7 hours per week

Week 1

Actuarial Statistics (CS1)

Derive the mean and variance of the main discrete distributions (binomial, Poisson, geometric, negative binomial, hypergeometric) from first principles using probability generating functions.
Compute probability generating functions for compound and mixed distributions and use them to recover moments.
Solve at least 15 past-paper-style problems on distribution fitting and moment matching under time pressure.
Build a one-page formula sheet linking pgf, mgf and moment relationships for discrete families.

A completed 20-question timed mock on discrete distributions, scored and error-logged with each mistake categorised by cause.

Week 2

Derive and apply the moment generating function for the normal, gamma, exponential and chi-squared distributions.
Apply the central limit theorem to approximate sums and averages, including continuity corrections.
Compute sampling distributions of the mean and variance for normal samples and use the t and F distributions correctly.
Work through at least 12 problems combining transformation of variables with standard distributions.

A written solutions portfolio of 12 transformation-of-variables problems with full derivations checked against the marking scheme style.

Week 3

Distinguish estimator properties: unbiasedness, consistency, efficiency and sufficiency, and prove each for given estimators.
Apply the Rao-Blackwell theorem and the factorisation criterion to find sufficient statistics.
Derive method-of-moments and maximum likelihood estimators for common models and check second-order conditions.
Compute Fisher information and the Cramer-Rao lower bound for at least six models.

A comparison table of MLE versus method-of-moments estimators for eight distributions, including bias and variance expressions derived by hand.

Week 4

Construct confidence intervals for means, proportions and variances in one-sample and two-sample settings.
Derive uniformly most powerful tests using the Neyman-Pearson lemma and likelihood ratio tests.
Compute power functions and determine sample sizes for specified power.
Interpret p-values and Type I and Type II error trade-offs in written explanations.

A 90-minute timed section on estimation and hypothesis testing, with a written reflection identifying the three weakest sub-topics.

Week 5

Fit simple and multiple linear regression models by least squares and derive the normal equations.
Derive and interpret standard errors, t-tests and F-tests for regression coefficients and overall fit.
Diagnose model assumptions using residual plots, leverage and Cook's distance concepts described numerically.
Perform one-way and two-way analysis of variance and interpret interaction terms.

A full regression and ANOVA problem set of 10 questions solved end to end with numerical answers to four significant figures.

Week 6

Apply generalised linear model concepts: link functions, linear predictors and exponential family form.
Fit and interpret logistic and Poisson regression outputs including deviance and AIC comparisons.
Distinguish Bayesian from frequentist inference and compute simple posterior distributions for conjugate priors.
Compute Bayes estimators under squared-error and absolute-error loss.

A one-page summary mapping each GLM component to its exponential family representation, plus three fully solved Bayesian conjugate-prior problems.

Week 7

Complete two full timed mock exams under exam conditions and mark them strictly against published mark allocations.
Re-solve every incorrect question from weeks 1 to 6 without notes.
Practise written explanation questions to build precision in stating assumptions and conclusions.
Identify and drill the two lowest-scoring sub-topics from the mock results.

Two marked mock papers with a consolidated error log and a targeted remediation list of no more than ten items.

Week 8

Review the formula sheet and error log daily, reciting key derivations from memory.
Complete one final timed mock and aim to beat the previous score by at least ten percentage points.
Rehearse exam timing strategy: allocating minutes per mark and flagging questions to revisit.
Confirm calculator procedures for distribution functions and regression routines.

A final mock exam scored at or above the target pass mark, plus a signed-off revision checklist covering every syllabus sub-topic.

Week 2: Score at least 60 percent on the week-2 discrete and continuous distribution mock, with all derivation errors corrected in the log.

Week 4: Complete the 90-minute estimation and hypothesis testing section within time and score at least 65 percent.

Week 6: Achieve at least 70 percent on the regression, GLM and Bayesian problem set, with numerical answers matching to four significant figures.

Week 8: Score at or above the target pass mark on the final timed mock and confirm every syllabus sub-topic is ticked on the revision checklist.