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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 Practice Questions
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