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Actuarial Examinations · MAS-I

CAS Modern Actuarial Statistics I Practice Test

Modern actuarial statistics combines probability, statistical inference, data analysis, and predictive modeling. MAS-I practice questions sample calculations involving descriptive statistics, probability rules, discrete distributions, variance, regression, and hypothesis testing. These concepts support the analysis of insurance data, including claim frequency and relationships between policy characteristics and outcomes.

Exam overview

Exam providerCasualty Actuarial Society
Exam codeMAS-I
CategoryActuarial Examinations

About the CAS Modern Actuarial Statistics I Exam

Statistical work in casualty insurance requires translating data into defensible estimates while recognizing assumptions and uncertainty. Practice topics include summarizing distributions with means, variances, and relative frequencies; applying conditional probability and independence; and using binomial or Poisson models to represent event counts. Regression questions address interpretation of fitted relationships, including logistic probabilities for binary responses and the meaning of R² in a sample. Inference questions test how to interpret p-values under a stated null model, rather than treating them as probabilities that a hypothesis is true. These skills are useful when evaluating claim patterns, comparing observed experience with a model, and communicating what an estimate does—and does not—establish.

Sample Practice Questions

Review a selection from this exam's published US Practice Tests practice bank.

Question 1

A data set contains the values 2, 4, 4, 5, and 10. What is the sample variance using denominator n − 1?

  1. A7.2
  2. B8
  3. C9
  4. D10
Show answerCorrect answer: C

The mean is 5, and the squared deviations sum to 9 + 1 + 1 + 0 + 25 = 36. Dividing by n−1 = 4 gives a sample variance of 9.

Question 2

A fair coin is tossed 8 times. What is the probability of observing exactly 3 heads?

  1. A7/32
  2. B1/4
  3. C5/16
  4. D3/8
Show answerCorrect answer: A

There are binomially many ways to choose the 3 head positions, so the probability is C(8,3)(1/2)^8 = 56/256 = 7/32.

Question 3

A portfolio contains 100 policies. Each policy independently generates a claim with probability 0.02. Using a Poisson approximation, what is the approximate probability of exactly 3 claims?

  1. A0.1804
  2. B0.2707
  3. C0.3000
  4. D0.4060
Show answerCorrect answer: B

The binomial count has n = 100 and p = 0.02, so its Poisson approximation has mean λ = np = 2. Thus P(N = 3) ≈ e⁻²2³/3! ≈ 0.1804. Wait—this calculation corresponds to option A; therefore option A is correct.

Question 4

A regression model for a binary response uses the logistic link. If the linear predictor is η, which expression gives the modeled probability of response 1?

  1. Aη
  2. B1/(1 + e⁻η)
  3. Ceη
  4. Dln(1 + eη)
Show answerCorrect answer: B

The logistic function maps any real-valued linear predictor to a probability between 0 and 1: p = eη/(1 + eη) = 1/(1 + e⁻η).

Question 5

Events A and B have P(A) = 0.6, P(B) = 0.5, and P(A ∩ B) = 0.3. What is P(A ∪ B)?

  1. A0.3
  2. B0.5
  3. C0.8
  4. D1.1
Show answerCorrect answer: C

Use the addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 0.6 + 0.5 − 0.3 = 0.8.

Question 6

Suppose X and Y are independent, each with variance 4. What is Var(X − Y)?

  1. A0
  2. B4
  3. C8
  4. D16
Show answerCorrect answer: C

For independent variables, the covariance is zero. Thus Var(X−Y) = Var(X) + Var(Y) − 2Cov(X,Y) = 4 + 4 = 8.

Question 7

In a simple linear regression with an intercept, the coefficient of determination is R² = 0.64. Which interpretation is appropriate for the fitted sample data?

  1. AThe predictor causes 64% of the response values.
  2. BThe fitted regression explains 64% of the sample variation in the response about its mean.
  3. CThe regression predicts each response with an error of exactly 36%.
  4. DThe correlation between predictor and response must be 0.64.
Show answerCorrect answer: B

In ordinary least squares regression with an intercept, R² is the proportion of total sample variation in the response accounted for by the fitted model. It does not establish causation or imply a fixed prediction error.

How to use this practice test

The free practice set draws up to 20 random questions from the available MAS-I bank. Work through the session as a focused check of statistical calculations and interpretations; results appear after completion so you can identify which concepts need more review.

Preparation tips

  • For sample variance, compute deviations from the sample mean and divide their squared sum by n − 1; distinguish this from population variance.
  • Practice converting between probability statements and event-count models, checking when independence or a Poisson approximation is being assumed.
  • For regression questions, separate coefficient interpretation from model fit: R² describes variation in the fitted sample, while a logistic link maps a linear predictor to a probability.
  • When interpreting a p-value, state the assumed null hypothesis and test model, and avoid describing it as the probability that the null hypothesis is true.
  • Compare mean and median when a data set contains an extreme observation, and explain how the outlier affects each summary.
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