PracticeVideosBlogFlashcardsEspañol
All Practice Exams

100+ Free IAI CS2 Practice Questions

Prepare for the IAI Subject CS2 Risk Modelling and Survival Analysis exam with instant access — no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately
100+ Questions
100% Free

Loading practice questions...

Same family resources

Explore More Institute of Actuaries of India Exams

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

ACET — Actuarial Common Entrance Test (Institute of Actuaries of India)

Practice Questions

IAI Subject CB1 — Business Finance (Institute of Actuaries of India)

Practice Questions

IAI Subject CB2 — Business Economics (Institute of Actuaries of India)

Practice Questions

IAI Subject CM1 — Actuarial Mathematics (Institute of Actuaries of India)

Practice Questions

IAI Subject CM2 — Financial Engineering and Loss Reserving (Institute of Actuaries of India)

Practice Questions

IAI Subject CP1 — Actuarial Practice (Institute of Actuaries of India)

Practice Questions
2026 Statistics

Key Facts: IAI CS2 Exam

5

Syllabus Areas

IAI CS2 syllabus

25%

Survival Models Weight

IAI CS2 syllabus

25%

Stochastic Processes Weight

IAI CS2 syllabus

3h15m

Paper A Duration

IAI CS2 syllabus

1h45m

Paper B Duration

IAI CS2 syllabus

R

Paper B Software

IAI CS2 syllabus

IAI Subject CS2 (Risk Modelling and Survival Analysis) is assessed through a 3-hour-15-minute paper-based Paper A and a 1-hour-45-minute computer-based Paper B in R, combined for a single result. The current syllabus, which mirrors IFoA CS2, weights Stochastic Processes and Survival Models most heavily at about 25% each, Random Variables/Distributions for Risk Modelling and Time Series at about 20% each, and Machine Learning at about 10%. IAI sets the pass mark and the INR exam fee separately for each diet rather than publishing fixed values.

Sample IAI CS2 Practice Questions

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

1In the Kaplan-Meier (product-limit) estimator of the survival function S(t), what role does a censored observation play at the moment of censoring?
A.It causes the survival estimate to drop by 1/n at the censoring time
B.It is removed from the dataset entirely and ignored in all calculations
C.It reduces the risk set for subsequent event times but does not itself cause a drop in the survival estimate
D.It is treated identically to a death at that time
Explanation: A right-censored observation contributes information up to the censoring time, so it remains in the risk set until censoring and then leaves it. Because no event (death) occurs, the product-limit factor (1 - d_j/n_j) is unchanged at that instant, so S(t) does not drop at a censoring time; it only steps down at observed event times.
2A study follows 10 lives. Deaths occur at t=2 (1 death) and t=5 (1 death), with one life censored at t=3. Using Kaplan-Meier, what is the estimated survival probability S(5)?
A.0.9000
B.0.8000
C.0.7000
D.0.7875
Explanation: At t=2 the risk set is 10 with 1 death, giving factor 9/10 = 0.9. The censoring at t=3 lowers the risk set but causes no drop. At t=5 the risk set is 10 - 1 death - 1 censored = 8 with 1 death, giving factor 7/8 = 0.875. Thus S(5) = 0.9 x 0.875 = 0.7875.
3The Nelson-Aalen estimator estimates which quantity directly?
A.The survival function S(t)
B.The cumulative hazard function H(t)
C.The probability density function f(t)
D.The force of mortality at a single point only
Explanation: The Nelson-Aalen estimator is a step function that estimates the cumulative (integrated) hazard H(t) = sum over event times of d_j/n_j. The survival function can then be recovered via S(t) = exp(-H(t)), but the Nelson-Aalen estimator itself targets the cumulative hazard.
4In the Cox proportional hazards model, the hazard is written lambda(t; z) = lambda_0(t) exp(beta^T z). What does the term lambda_0(t) represent?
A.The baseline hazard, common to all individuals when all covariates are zero
B.The cumulative hazard for the highest-risk individual
C.A covariate-specific multiplier that varies by individual
D.The probability of survival to time t
Explanation: lambda_0(t) is the baseline hazard, the hazard for an individual whose covariates are all zero. The exponential factor exp(beta^T z) scales this baseline up or down according to each individual's covariates, which is why the model is 'proportional' hazards.
5A key advantage of the Cox proportional hazards model over fully parametric survival models is that it:
A.Requires the baseline hazard to be exponential
B.Cannot handle censored data
C.Estimates the regression coefficients without specifying the form of the baseline hazard
D.Always produces a constant hazard over time
Explanation: The Cox model is semi-parametric: it estimates the covariate coefficients beta via partial likelihood without assuming any functional form for lambda_0(t). This flexibility is its main appeal, since the proportional-hazards structure is preserved regardless of the baseline shape.
6In the two-state (alive-dead) Markov model of mortality, the maximum likelihood estimate of the constant force of mortality mu is given by:
A.Number of deaths divided by the initial number of lives
B.Total waiting time divided by number of deaths
C.The square root of the number of deaths
D.Number of deaths divided by total waiting time (central exposed to risk)
Explanation: Under the two-state model with constant force mu, deaths follow a Poisson-type likelihood and the MLE is mu-hat = D / E^c_x, where D is the observed number of deaths and E^c_x is the central exposed to risk (total time lives are observed alive). This is the classic occurrence-exposure rate.
7The central exposed to risk E^c_x differs from the initial exposed to risk E_x principally because:
A.Central exposed to risk ignores all deaths during the year
B.Initial exposed to risk is always larger by exactly the number of new entrants
C.Central exposed to risk counts time observed, ending at death/exit, while initial exposed to risk extends a deceased life's contribution to the end of the rate interval
D.They are identical and the distinction is purely notational
Explanation: Central exposed to risk measures the actual person-time lives spend under observation, terminating at death. Initial exposed to risk adds, for each death, the remaining fraction of the rate interval, since under the q_x convention a life is assumed exposed for the whole year of age in which it dies. Hence E_x = E^c_x + (deaths' remaining time).
8Graduation of crude mortality rates is performed primarily to:
A.Increase the number of deaths in each age group
B.Remove all censored observations from the dataset
C.Produce a smooth set of rates that progress regularly with age while remaining adherent to the data
D.Convert forces of mortality into survival probabilities
Explanation: Graduation smooths crude (raw) rates so that mortality progresses smoothly by age, reflecting the belief that the underlying rates vary regularly. The graduated rates must balance smoothness against adherence (goodness of fit) to the observed crude rates.
9Which statistical test is commonly used after graduation to check whether the graduated rates adhere to the crude data overall by examining standardised deviations?
A.The chi-squared test
B.The Kaplan-Meier log-rank test
C.The Durbin-Watson test
D.The Dickey-Fuller test
Explanation: The chi-squared test sums the squared standardised deviations z_x = (actual - expected)/sqrt(expected) across age groups and compares the total to a chi-squared distribution. It is a primary overall goodness-of-fit test for a graduation, though it must be supplemented by tests for runs, bias and individual large deviations.
10The 'signs test' applied to graduation residuals primarily detects:
A.Overall bias (an excess of positive or negative deviations)
B.The presence of a unit root
C.Heteroscedasticity in the deviations
D.The exact magnitude of the largest deviation
Explanation: The signs test counts the number of positive deviations and compares it to a Binomial(n, 0.5) distribution. A significant imbalance indicates overall bias in the graduation, meaning the graduated rates are systematically above or below the crude rates.

About the IAI CS2 Exam

IAI Subject CS2, Risk Modelling and Survival Analysis, is a Core Principles actuarial exam covering survival models, Markov and multiple-state processes, time series, loss distributions, extreme value theory, copulas, run-off triangles, and a high-level overview of machine learning, mirroring the IFoA CS2 curriculum in the Indian jurisdiction.

Assessment

Paper A written exam (varying-mark questions) plus Paper B computer-based R modelling exam, combined for one result

Time Limit

3 hours 15 minutes (Paper A) plus 1 hour 45 minutes (Paper B)

Passing Score

IAI sets the pass mark for each diet on the combined Paper A and Paper B result; no fixed percentage is published

Exam Fee

Set in INR by IAI each examination diet; consult the current IAI fee schedule (Institute of Actuaries of India (IAI))

IAI CS2 Exam Content Outline

25%

Stochastic Processes

Markov chains and Markov jump processes, the Markov property, holding times, absorbing and recurrent states, Kolmogorov and Chapman-Kolmogorov equations, counting and Poisson processes, Brownian motion, and multiple-state models with transition-intensity estimation.

25%

Survival Models

The two-state mortality model, central and initial exposed to risk, the principle of correspondence, Kaplan-Meier and Nelson-Aalen estimators, censoring types, the Cox proportional hazards model, and graduation with the chi-squared, signs, and runs tests.

20%

Random Variables and Distributions for Risk Modelling

Loss distributions such as Pareto and lognormal, reinsurance arrangements, the collective and compound risk models, extreme value theory with the GEV and Generalised Pareto distributions, copulas, tail dependence, and run-off triangles for reserving.

20%

Time Series

Stationarity and autocovariance, AR, MA, ARMA and ARIMA models, the ACF and PACF, the Box-Jenkins methodology, unit roots and the Dickey-Fuller test, cointegration, exponential smoothing, and forecasting diagnostics.

10%

Machine Learning

A high-level overview of supervised and unsupervised learning, the bias-variance trade-off, overfitting, cross-validation, decision trees, random forests, boosting, regularisation, and their relevance to actuarial data analysis in R.

How to Pass the IAI CS2 Exam

What You Need to Know

  • Passing score: IAI sets the pass mark for each diet on the combined Paper A and Paper B result; no fixed percentage is published
  • Assessment: Paper A written exam (varying-mark questions) plus Paper B computer-based R modelling exam, combined for one result
  • Time limit: 3 hours 15 minutes (Paper A) plus 1 hour 45 minutes (Paper B)
  • Exam fee: Set in INR by IAI each examination diet; consult the current IAI fee schedule

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

IAI CS2 Study Tips from Top Performers

1Build fluency with exposed-to-risk concepts: know exactly when to use the central exposed to risk for the force mu and the initial exposed to risk for the probability q_x, and apply the principle of correspondence.
2Learn the Kaplan-Meier and Nelson-Aalen estimators by hand on small censored datasets so the risk-set bookkeeping and the link S(t) = exp(-H(t)) become automatic.
3For graduation, practise selecting the right test: chi-squared for overall fit, the signs test for bias, and the runs test for clustering of same-sign deviations.
4Drill the ACF/PACF signatures: AR(p) has a PACF that cuts off at p, while MA(q) has an ACF that cuts off at q, and always check stationarity before fitting an ARMA model.
5Spend dedicated time in R replicating survival, time-series and loss-model fits, since the Paper B component is marked on practical data analysis, not just theory.

Frequently Asked Questions

How is IAI Subject CS2 examined?

CS2 is examined in two parts that combine for one result: Paper A, a 3-hour-15-minute paper-based written exam, and Paper B, a 1-hour-45-minute computer-based exam in which candidates analyse real data using R.

What topics does IAI CS2 cover?

CS2 covers survival models (Kaplan-Meier, Nelson-Aalen, Cox), Markov and multiple-state stochastic processes, time series, loss distributions, extreme value theory, copulas, run-off triangles, and a high-level overview of machine learning.

Which CS2 topics carry the most marks?

Stochastic Processes and Survival Models are each weighted at about 25%. Random Variables/Distributions for Risk Modelling and Time Series are each about 20%, and Machine Learning is the smallest area at about 10%.

What is the passing score for IAI CS2?

IAI sets the pass mark for each examination diet based on the combined Paper A and Paper B performance and does not publish one fixed percentage. The conventional target is broadly in the 50-60% range.

Does IAI CS2 require R?

Yes. The computer-based Paper B component requires candidates to carry out practical data analysis and statistical actuarial modelling using the R programming language, so R proficiency is essential.

Is IAI CS2 the same as IFoA CS2?

IAI Subject CS2 mirrors the IFoA CS2 (Risk Modelling and Survival Analysis) Core Principles curriculum, applied within the Indian jurisdiction. The syllabus structure, topic areas and weightings are closely aligned.