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In a normal linear regression, an approximate 95% prediction interval for a new observation is wider than the corresponding confidence interval for the mean response because it includes:

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B
C
D
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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

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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.

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