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100+ Free IAI CS1 Practice Questions

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2026 Statistics

Key Facts: IAI CS1 Exam

2

Combined Components

IAI CS1 format

3h 15m

CS1A Written Time

IAI CS1 format

1h 45m

CS1B R Exam Time

IAI CS1 format

R

CS1B Software

IAI CS1 syllabus

Core

Principles Subject

IAI qualification

100

Practice Questions

OpenExamPrep

IAI Subject CS1 Actuarial Statistics is examined in two combined components: a CS1A written theory paper of 3 hours 15 minutes and a CS1B computer-based exam of 1 hour 45 minutes that requires the R statistical software, both marked together for one CS1 result. The curriculum mirrors the IFoA CS1 syllabus in the India jurisdiction and weights application skills heavily over pure recall. IAI does not publish a fixed question count or a fixed pass mark; the pass standard is set each diet. This free set provides 100 multiple-choice questions across the full CS1 theory body of knowledge.

Sample IAI CS1 Practice Questions

Try these sample questions to test your IAI CS1 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A discrete random variable X follows a Poisson distribution with mean lambda = 3. What is the variance of X?
A.1.73
B.3
C.9
D.6
Explanation: For a Poisson distribution the variance equals the mean, so Var(X) = lambda = 3. This equidispersion property is a defining feature of the Poisson model and is why it is used as a baseline for count data.
2If X ~ Binomial(n=10, p=0.3), what is the expected value E(X)?
A.0.3
B.7
C.2.1
D.3
Explanation: The mean of a binomial distribution is np = 10 x 0.3 = 3. The expected number of successes scales linearly with both the number of trials and the success probability.
3The moment generating function (MGF) of a random variable is M(t) = exp(2t + 3t^2/2). Which distribution does X follow?
A.Normal with mean 2 and variance 3
B.Normal with mean 3 and variance 2
C.Exponential with rate 2
D.Gamma with parameters 2 and 3
Explanation: The MGF of a Normal(mu, sigma^2) is exp(mu t + sigma^2 t^2/2). Matching terms gives mu = 2 and sigma^2 = 3, so X ~ N(2, 3).
4For an exponential distribution with rate parameter lambda = 0.5, what is the median?
A.2
B.1.386
C.0.5
D.0.693
Explanation: The median m solves F(m) = 1 - exp(-lambda m) = 0.5, giving m = ln(2)/lambda = 0.6931/0.5 = 1.386. The exponential median is always less than its mean (which is 1/lambda = 2) because the distribution is right-skewed.
5Which property uniquely characterises the exponential distribution among continuous distributions?
A.Memorylessness
B.Symmetry about the mean
C.Bounded support
D.Finite higher moments only
Explanation: The exponential distribution is the only continuous distribution with the memoryless property: P(X > s + t | X > s) = P(X > t). This makes it the natural model for waiting times with constant hazard.
6X and Y are independent with Var(X) = 4 and Var(Y) = 9. What is Var(2X - Y)?
A.17
B.25
C.7
D.13
Explanation: For independent variables, Var(2X - Y) = 4 Var(X) + Var(Y) = 4(4) + 9 = 25. Constants are squared when factored out of the variance operator and there is no covariance term under independence.
7A continuous random variable has pdf f(x) = 3x^2 for 0 <= x <= 1. What is E(X)?
A.0.5
B.0.25
C.0.6
D.0.75
Explanation: E(X) = integral of x times 3x^2 from 0 to 1 = integral of 3x^3 = [3x^4/4] from 0 to 1 = 3/4 = 0.75. This Beta(3,1) distribution is concentrated toward 1, so a mean above 0.5 is expected.
8The skewness of a Gamma(alpha, beta) distribution is given by which expression?
A.2/sqrt(alpha)
B.1/alpha
C.alpha/beta
D.sqrt(alpha)/2
Explanation: The coefficient of skewness for a Gamma distribution is 2/sqrt(alpha), depending only on the shape parameter alpha. As alpha increases the distribution becomes more symmetric, consistent with its convergence toward normality.
9If Z ~ N(0,1), what is P(-1.96 < Z < 1.96) approximately?
A.0.90
B.0.99
C.0.95
D.0.975
Explanation: The interval (-1.96, 1.96) captures the central 95% of the standard normal distribution, leaving 2.5% in each tail. This is the basis of the standard 95% confidence interval.
10A random variable X has a lognormal distribution if which transformation is normally distributed?
A.X^2
B.ln(X)
C.1/X
D.sqrt(X)
Explanation: X is lognormal precisely when ln(X) follows a normal distribution. The lognormal is widely used in actuarial work to model positively skewed quantities such as claim sizes.

About the IAI CS1 Exam

IAI Subject CS1 Actuarial Statistics is a Core Principles subject that grounds candidates in statistical distributions, data analysis, statistical inference, linear and generalised linear regression, Bayesian statistics, correlation and copulas, and basic time-series concepts used in actuarial work.

Assessment

Two combined components: CS1A written paper plus CS1B computer-based R exam

Time Limit

CS1A 3 hours 15 minutes; CS1B 1 hour 45 minutes

Passing Score

IAI does not publish a fixed pass mark; CS1A and CS1B are combined and graded against a pass standard set each diet

Exam Fee

Set by IAI in INR each sitting; see the official IAI examination notice (Institute of Actuaries of India (IAI))

IAI CS1 Exam Content Outline

20-25%

Random Variables and Distributions

Study discrete and continuous distributions, expectation, variance, moments, generating functions, transformations, and standard actuarial models such as the Poisson, binomial, exponential, gamma, and lognormal distributions.

30-35%

Data Analysis and Statistical Inference

Work with descriptive statistics, point and interval estimation, maximum likelihood, sampling distributions, hypothesis tests, the central limit theorem, and chi-squared goodness-of-fit and contingency-table tests.

20-25%

Regression and Generalised Linear Models

Apply simple and multiple linear regression, least squares, residual diagnostics, model selection, and generalised linear models with link functions and variance functions for Poisson, binomial, and gamma responses.

20-25%

Bayesian Statistics, Correlation and Time Series

Use Bayes theorem, conjugate priors, loss functions, credible intervals and credibility theory, measures of correlation and copulas, and basic stationary time-series concepts including AR, MA, and random-walk behaviour.

How to Pass the IAI CS1 Exam

What You Need to Know

  • Passing score: IAI does not publish a fixed pass mark; CS1A and CS1B are combined and graded against a pass standard set each diet
  • Assessment: Two combined components: CS1A written paper plus CS1B computer-based R exam
  • Time limit: CS1A 3 hours 15 minutes; CS1B 1 hour 45 minutes
  • Exam fee: Set by IAI in INR each sitting; see the official IAI examination notice

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 CS1 Study Tips from Top Performers

1Treat CS1 as an application subject. The assessment weighting favours applying methods over reciting definitions, so practise full problem set-ups rather than memorising formulas in isolation.
2Build genuine R fluency for CS1B. Practise fitting linear models and GLMs, producing diagnostic plots, and reading the software output, because the practical paper rewards speed and accuracy in R.
3Master the standard distributions cold. Knowing the means, variances, generating functions, and link to actuarial use of the Poisson, binomial, exponential, gamma, and lognormal saves time across the whole paper.
4For inference, always identify whether the variance is known, the sample is small, and whether you need a one-sided or two-sided test before choosing the z, t, chi-squared, or F reference distribution.
5Learn the conjugate-prior pairings (Beta-binomial, Gamma-Poisson, normal-normal) so Bayesian updating becomes a quick parameter change rather than a full integration under time pressure.

Frequently Asked Questions

What is the format of the IAI CS1 exam?

CS1 has two combined components. CS1A is a written paper of statistical theory lasting 3 hours 15 minutes, and CS1B is a computer-based exam of 1 hour 45 minutes that requires you to apply methods using the R statistical software. Both are taken in the same diet and marked together for one CS1 result.

How many questions are on IAI CS1?

IAI does not publish a fixed question count. CS1A contains a mix of written statistical-theory questions and CS1B contains computer-based R tasks. This free set provides 100 multiple-choice questions covering the same body of knowledge for revision.

What is the passing score for IAI CS1?

IAI does not publish a fixed numerical pass mark. The CS1A and CS1B components are combined and graded against a pass standard that the examiners set for each diet, so candidates should focus on mastering the syllabus rather than a fixed percentage.

Which topics matter most on CS1?

Statistical inference and the properties of distributions carry substantial weight, followed by regression and generalised linear models. Bayesian statistics, correlation and copulas, and basic time series complete the syllabus, and the assessment is weighted heavily toward application rather than recall.

Do I need R for IAI CS1?

Yes. The CS1B component is a computer-based exam that requires you to carry out statistical analysis using the R software. Strong familiarity with R data handling, model fitting, and output interpretation is essential alongside the CS1A theory.

How does IAI CS1 relate to the IFoA CS1?

IAI CS1 mirrors the Institute and Faculty of Actuaries CS1 Actuarial Statistics syllabus in the India jurisdiction. The body of knowledge, topic structure, and CS1A and CS1B component design are aligned with the IFoA Core Principles framework.