IFoA CM2 study plan

Derive and interpret the Chapman-Kolmogorov equations and compute n-step transition probabilities for a small state space by hand and in code

Classify states (transient, recurrent, periodic, absorbing) and compute hitting probabilities and expected hitting times for a 3-4 state chain

Set up the generator matrix of a Markov jump process and derive the Kolmogorov forward equations for a simple illness-death model

Map the modelling cycle (specify, fit, validate, communicate) onto one Markov model example and list the assumptions each step makes

Write a one-page assumption audit template you will reuse for later models

Solve jump-process transition probability problems using matrix exponentials or Laplace transforms for 2-3 state models

Estimate transition intensities from aggregate exposed-to-risk data and state the assumptions behind the estimator

Define weak and strict stationarity and test a given series description against each definition

Fit and interpret AR, MA and ARMA models up to order 2, including stationarity and invertibility conditions

Compute autocovariance and autocorrelation functions for an AR(1) and an MA(1) from first principles

Derive the Kaplan-Meier product-limit estimator and construct Greenwood confidence intervals for a small dataset

Distinguish censoring types and explain which estimators remain valid under each

Build a life table from raw deaths and exposure data, computing central exposed-to-risk and qx from mx

Compare the Cox proportional hazards model with parametric survival models and interpret hazard ratios

Apply differencing and ARIMA(p,d,q) identification to a non-stationary series and justify the chosen d

Derive ordinary least squares estimators in matrix form and state the Gauss-Markov conditions

Diagnose heteroscedasticity, non-linearity and influential points from residual summaries and state the corrective model change

Specify and interpret a generalised linear model: link function, linear predictor, variance function and deviance

Distinguish method of moments, maximum likelihood and least squares estimators, and evaluate bias, variance and consistency for each

Derive the Cramer-Rao lower bound and use it to compare two candidate estimators

Compute maximum likelihood estimates and their asymptotic standard errors for binomial, Poisson and normal samples

Construct and interpret confidence intervals using pivots, and explain the coverage probability of an interval

Set up a likelihood ratio test and a Wald test for a composite null and compare their conclusions

Explain size, power and p-value correctly, and compute the power of a simple test against a specified alternative

Identify when a normal approximation is inappropriate and select an exact alternative

Fit binomial and Poisson models by maximum likelihood and test goodness of fit using deviance and the chi-square approximation

Derive the mean and variance of the Poisson and binomial distributions and state the Poisson limit of the binomial

Transform and combine normal variables, and compute probabilities for sums and sample means

Use the lognormal, chi-square, t and F distributions in the contexts where each arises in CM2

Explain overdispersion in a Poisson model and describe the quasi-Poisson and negative binomial responses

Graduate a set of crude mortality rates using at least two methods and compare the fitted-versus-actual residuals

State the criteria for a valid graduation: adherence, smoothness, parsimony and comparability with the standard table

Apply a mortality projection model and interpret the resulting improvement factors and cohort effects

Explain the Lee-Carter structure and the role of the time index in projecting future rates

Adjust a life table for selection effects and describe the impact on annuity values

Assemble a formula and assumption summary across all ten domains, flagging the three you are least confident in

Complete two full-length timed mock papers under exam conditions and record scores by domain

Rework every mock question answered incorrectly until you can reproduce the method unaided

Rehearse written explanations of model assumptions and limitations for the higher-mark discussion parts

Finalise a one-page exam-day checklist covering calculator, formula list and time allocation