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2026 Statistics

Key Facts: IFoA CS2 Exam

2 papers

Paper A + Paper B

IFoA curriculum

3h20

Paper A Time

IFoA curriculum

1h50

Paper B Time (R)

IFoA curriculum

70:30

Theory to Problem Split

IFoA marking

5

Syllabus Areas

IFoA 2026 syllabus

25%

Largest Domains

IFoA 2026 syllabus

CS2 Risk Modelling and Survival Analysis is an IFoA Core Principles subject assessed in one sitting by Paper A, a 3 hour 20 minute Word-based theory exam, and Paper B, a 1 hour 50 minute problem-based assessment using Word and R. The 2026 IFoA syllabus weights Stochastic Processes and Survival Models most heavily at about 25% each, with Random Variables and Distributions for Risk Modelling and Time Series each around 20% and Machine Learning about 10%. The two papers are marked and aggregated with a 70:30 theory-to-problem split into a single CS2 result, and the IFoA does not publish a fixed pass mark.

Sample IFoA CS2 Practice Questions

Try these sample questions to test your IFoA CS2 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1For a Pareto distribution with parameters α and λ, which property makes it a popular model for large insurance losses?
A.It has a heavy (slowly decaying) tail, capturing the chance of very large claims
B.It is bounded above, so claims cannot exceed a fixed maximum
C.Its mean always equals its variance
D.It is symmetric about its median
Explanation: The Pareto distribution has a power-law tail that decays slowly, so it assigns non-negligible probability to extreme losses, making it suitable for modelling large or catastrophic claims. Its moments exist only for α greater than the moment order.
2Under proportional reinsurance with retention proportion a (0 < a < 1), if the gross claim is X, what amount does the insurer retain?
A.(1 - a)X
B.aX
C.max(X - a, 0)
D.min(X, a)
Explanation: Proportional (quota share) reinsurance splits every claim in fixed proportions. The insurer retains aX and the reinsurer pays (1 - a)X, regardless of claim size. This contrasts with excess-of-loss, which depends on a retention level.
3Under excess-of-loss reinsurance with retention M, the reinsurer pays Z = max(X - M, 0). If individual claims X are exponential with mean 1/λ, what is the probability that the reinsurer is involved in a given claim?
A.1 - e^{-λM}
B.λM
C.e^{-λM}
D.1 - λM
Explanation: The reinsurer is involved when X > M. For an exponential distribution, P(X > M) = e^{-λM}. The memoryless property also means the conditional excess X - M given X > M is again exponential with the same rate λ.
4In the collective risk model, aggregate claims S = X1 + ... + XN where N is the claim number and Xi are i.i.d. claim sizes independent of N. Which formula gives E[S]?
A.E[N] + E[X]
B.Var(N) × E[X]
C.E[N] × Var(X)
D.E[N] × E[X]
Explanation: By the tower/conditional-expectation rule, E[S] = E[N]E[X]. This is the standard compound-distribution mean. The variance uses E[S] differently: Var(S) = E[N]Var(X) + Var(N)E[X]^2.
5For a compound Poisson aggregate-claims distribution S with Poisson parameter λ and claim sizes X, which expression gives Var(S)?
A.λ E[X]
B.λ E[X^2]
C.λ Var(X)
D.λ^2 E[X]^2
Explanation: For a compound Poisson, Var(N) = E[N] = λ, so Var(S) = λVar(X) + λE[X]^2 = λ(Var(X) + E[X]^2) = λE[X^2]. This compact result is a hallmark of the compound Poisson model.
6A copula is used in CS2 to model dependence between random variables. According to Sklar's theorem, a copula C links the joint distribution F to the marginals because:
A.F(x, y) = C(x, y) for all x, y
B.C(u, v) = F_X(u) + F_Y(v)
C.F(x, y) = C(F_X(x), F_Y(y)) where F_X, F_Y are the marginal CDFs
D.C(u, v) = F_X(u) × F_Y(v) always
Explanation: Sklar's theorem states any multivariate CDF can be written as F(x,y) = C(F_X(x), F_Y(y)), where the copula C is a CDF on [0,1]^2 with uniform marginals. This separates the dependence structure (the copula) from the marginal behaviour.
7Which copula is particularly suited to modelling upper tail dependence, i.e. the tendency of large losses to occur together?
A.The Gaussian copula
B.The Fréchet lower-bound copula
C.The independence copula
D.The Gumbel copula
Explanation: The Gumbel copula exhibits upper tail dependence, making it useful where extreme high values are correlated (e.g. simultaneous large insurance losses). The Clayton copula, by contrast, captures lower tail dependence.
8In extreme value theory, the Pickands-Balkema-de Haan theorem states that the distribution of excesses over a high threshold converges to which family?
A.The Generalised Pareto Distribution (GPD)
B.The Generalised Extreme Value (GEV) distribution
C.The normal distribution
D.The Poisson distribution
Explanation: The Pickands-Balkema-de Haan theorem underpins the peaks-over-threshold (POT) approach: for a high enough threshold u, the conditional distribution of X - u given X > u tends to a Generalised Pareto Distribution. The GEV instead arises as the limit for block maxima.
9The Generalised Extreme Value (GEV) distribution unifies three types. Which shape parameter ξ value corresponds to the Fréchet (heavy-tailed) type?
A.ξ < 0
B.ξ = 0
C.ξ > 0
D.ξ = 1 only
Explanation: The GEV shape parameter ξ classifies the tail: ξ > 0 gives the Fréchet type (heavy tail, e.g. for large losses), ξ = 0 gives the Gumbel type (light tail), and ξ < 0 gives the Weibull type (bounded upper tail).
10Which measure of upper tail dependence λ_U for two variables with copula C is defined as the limit lim_{u→1} P(U > u | V > u)?
A.It always equals the linear correlation coefficient
B.It equals Kendall's tau
C.It equals C(u,u) at u = 0.5
D.It equals lim_{u→1} (1 - 2u + C(u,u)) / (1 - u)
Explanation: The coefficient of upper tail dependence is λ_U = lim_{u→1} P(U > u | V > u) = lim_{u→1} (1 - 2u + C(u,u))/(1 - u). A positive λ_U indicates extremes tend to occur jointly; λ_U = 0 means asymptotic independence in the upper tail.

About the IFoA CS2 Exam

IFoA Subject CS2, Risk Modelling and Survival Analysis, is a Core Principles actuarial subject covering risk models, stochastic processes, survival analysis, time series, and machine learning, assessed by a theory paper and an R-based problem paper.

Assessment

Paper A theory exam (Word) plus Paper B problem-based assessment (Word and R), taken in the same sitting

Time Limit

Paper A 3 hours 20 minutes and Paper B 1 hour 50 minutes

Passing Score

No fixed pass mark is published; Paper A and Paper B marks are aggregated 70:30 into a single CS2 result with the pass mark set each session

Exam Fee

Set in the IFoA fees schedule each session; confirm the current Associate-level exam fee on the IFoA site (Institute and Faculty of Actuaries (IFoA))

IFoA CS2 Exam Content Outline

20%

Random Variables and Distributions for Risk Modelling

Work with loss distributions, deductibles and reinsurance, the collective and individual risk models, compound distributions, copulas, extreme value theory, and risk measures such as Value at Risk and Expected Shortfall.

20%

Time Series

Analyse stationarity and autocovariance, fit ARMA and ARIMA models using the Box-Jenkins approach, identify orders from the ACF and PACF, run residual diagnostics, and produce forecasts including cointegration concepts.

25%

Stochastic Processes

Apply Markov chains and Markov jump processes, including transition matrices, communicating classes, stationary distributions, holding times, generator matrices, the Kolmogorov equations, and counting processes.

25%

Survival Models

Use the survival function and hazard, Kaplan-Meier and Nelson-Aalen estimators, Cox proportional hazards regression, exposed-to-risk, graduation and its statistical tests, and mortality projection methods such as Lee-Carter.

10%

Machine Learning

Understand supervised and unsupervised learning, the bias-variance trade-off, overfitting, cross-validation, regularisation, decision trees and ensembles, and the basics of neural networks.

How to Pass the IFoA CS2 Exam

What You Need to Know

  • Passing score: No fixed pass mark is published; Paper A and Paper B marks are aggregated 70:30 into a single CS2 result with the pass mark set each session
  • Assessment: Paper A theory exam (Word) plus Paper B problem-based assessment (Word and R), taken in the same sitting
  • Time limit: Paper A 3 hours 20 minutes and Paper B 1 hour 50 minutes
  • Exam fee: Set in the IFoA fees schedule each session; confirm the current Associate-level exam fee on the IFoA site

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

IFoA CS2 Study Tips from Top Performers

1Treat survival models and stochastic processes as the priority, because together they make up about half of the CS2 syllabus and reward fluent, automatic setups under time pressure.
2Practise Paper B style problems directly in R, not just on paper, so that fitting models, producing Kaplan-Meier estimates, and running diagnostics become routine in RStudio.
3Link the Markov jump process framework to survival analysis: the force of mortality is a transition intensity, and many estimators reduce to an occurrence-over-exposure ratio.
4For time series, drill identifying ARMA and ARIMA orders from the ACF and PACF, then confirm fit with residual diagnostics such as the Ljung-Box test.
5Do not neglect machine learning despite its smaller weight; the bias-variance trade-off, cross-validation, and regularisation are high-yield, quotable concepts that recur in examiner reports.

Frequently Asked Questions

What is the format of the IFoA CS2 exam?

CS2 has two computer-based papers taken in the same sitting: Paper A is a Word-based theory exam and Paper B is a problem-based assessment using Word and R. Both elements must be attempted together for a valid CS2 result.

How long are the CS2 papers?

Paper A lasts 3 hours 20 minutes and Paper B lasts 1 hour 50 minutes, each including a short additional allowance to download or print the paper. Both are sat in the same examination session.

What is the pass mark for CS2?

The IFoA does not publish a fixed pass mark. Paper A and Paper B are marked and aggregated with a 70:30 split between the theory and problem-based papers into a single CS2 mark, and the pass mark is set for each session.

Which topics matter most on CS2?

Stochastic Processes and Survival Models are the largest areas at roughly 25% each. Random Variables and Distributions for Risk Modelling and Time Series are each around 20%, and Machine Learning accounts for about 10%.

Do I need R for CS2?

Yes. Paper B is a problem-based assessment that requires R, and the IFoA advises candidates to be familiar with RStudio. CS2 builds on the R and statistics foundation introduced in CS1.

How does CS2 fit into the IFoA qualifications?

CS2 is one of the Core Statistics subjects within the IFoA Associate (AIA) qualification, sitting alongside CS1. It covers the actuarial statistics and modelling techniques used across later subjects.