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100+ Free MAS-I Practice Questions

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Question 1
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If X is a discrete random variable with P(X=0)=0.4, P(X=1)=0.4, and P(X=2)=0.2, what is E[X]?

A
B
C
D
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Key Facts: MAS-I Exam

~45 Qs

Multiple Choice

4-hour CBT format

30-40%

Recent Pass Rate

CAS sittings

300-500 hrs

Typical Study Time

ACAS candidate average

~$1,000

Total Exam Cost

CAS fee schedule

2x/year

Sitting Windows

April-May and October-November

6-10

Pass Score Range

CAS 0-10 scale

CAS Exam MAS-I is a 4-hour, ~45-question computer-based exam administered by the Casualty Actuarial Society in the Spring (April-May) and Fall (October-November) windows. Topic weights are Probability Models 20%, Stochastic Processes 20%, Statistics & Estimation 20%, Confidence Intervals & Hypothesis Testing 15%, Linear Regression 15%, and Time Series 10%. CAS reports results on a 0-10 scale with 6-10 indicating pass. The exam fee runs roughly $1,000, and most candidates spend 300-500 hours preparing. MAS-I is required to advance toward the ACAS designation.

Sample MAS-I Practice Questions

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

1If X is a discrete random variable with P(X=0)=0.4, P(X=1)=0.4, and P(X=2)=0.2, what is E[X]?
A.0.6
B.0.8
C.1.0
D.1.2
Explanation: E[X] = 0(0.4) + 1(0.4) + 2(0.2) = 0 + 0.4 + 0.4 = 0.8. The expected value of a discrete random variable is the probability-weighted sum of its possible values.
2X follows a Poisson distribution with mean 4. What is Var(X)?
A.2
B.4
C.8
D.16
Explanation: For a Poisson distribution, Var(X) = E[X] = λ. Since the mean is 4, the variance is also 4. This equality of mean and variance is a defining property of the Poisson distribution.
3X ~ Exponential(λ=2). What is E[X]?
A.0.5
B.1
C.2
D.4
Explanation: For the exponential distribution with rate parameter λ, E[X] = 1/λ. With λ=2, E[X] = 1/2 = 0.5. The variance is 1/λ² = 0.25.
4Which distribution would best model the number of independent Bernoulli(p) trials needed to obtain the first success?
A.Binomial
B.Geometric
C.Poisson
D.Negative Binomial with r=2
Explanation: The geometric distribution models the number of trials needed for the first success in a sequence of independent Bernoulli(p) trials. Its PMF is P(X=k) = (1-p)^(k-1)·p for k=1, 2, 3, …
5The moment generating function (MGF) of a random variable X is defined as:
A.M(t) = E[tX]
B.M(t) = E[e^(tX)]
C.M(t) = E[X^t]
D.M(t) = E[ln(tX)]
Explanation: The MGF is M(t) = E[e^(tX)], defined wherever the expectation exists in a neighborhood of 0. Moments are recovered by differentiating: E[X^n] = M^(n)(0). MGFs uniquely determine the distribution when they exist.
6If X ~ Normal(μ=10, σ²=4), what is P(X > 12) approximately?
A.0.1587
B.0.3085
C.0.5000
D.0.8413
Explanation: Standardize: Z = (12-10)/2 = 1. From the standard normal table, P(Z > 1) ≈ 0.1587. Note σ = √4 = 2, not 4, so the denominator is 2.
7For X ~ Gamma(α, β) with E[X] = αβ and Var(X) = αβ², what is the coefficient of variation?
A.1/√α
B.1/α
C.√α
D.β
Explanation: Coefficient of variation (CV) = SD/Mean = √(αβ²)/(αβ) = β√α/(αβ) = 1/√α. The CV depends only on the shape parameter α, not the scale β.
8X is a mixture: with probability 0.3, X ~ Exp(1); with probability 0.7, X ~ Exp(2). What is E[X]?
A.0.65
B.0.50
C.0.30
D.1.50
Explanation: For a mixture, E[X] = Σ wᵢ·E[Xᵢ]. Here E[X] = 0.3(1/1) + 0.7(1/2) = 0.3 + 0.35 = 0.65. The mixture mean is the weighted average of component means.
9For X ~ Lognormal(μ, σ²), which statement is TRUE?
A.ln(X) is normally distributed with mean μ and variance σ²
B.X is normally distributed with mean μ
C.E[X] = μ
D.X can take negative values
Explanation: By definition, X is lognormal if ln(X) ~ Normal(μ, σ²). Therefore X > 0 always, E[X] = exp(μ + σ²/2), and X itself is not normal. The parameter μ is the mean of the underlying normal, not of X.
10If X and Y are independent with MGFs M_X(t) and M_Y(t), the MGF of S = X + Y is:
A.M_X(t) + M_Y(t)
B.M_X(t)·M_Y(t)
C.M_X(t)/M_Y(t)
D.M_X(t)^M_Y(t)
Explanation: For independent X and Y, M_S(t) = E[e^(t(X+Y))] = E[e^(tX)]·E[e^(tY)] = M_X(t)·M_Y(t). The MGF of a sum of independent variables is the product of their MGFs.

About the MAS-I Exam

CAS Exam MAS-I (Modern Actuarial Statistics I) is the first of two CAS modern statistics exams on the ACAS credentialing pathway. The 4-hour computer-based exam contains roughly 45 multiple-choice questions covering probability models, stochastic processes (Markov chains, Poisson processes), statistical estimation (MLE, method of moments), confidence intervals, hypothesis testing, linear regression, and time series analysis. Pass rates typically run 30-40%.

Questions

45 scored questions

Time Limit

4 hours (CBT)

Passing Score

Scaled (~6/10 typical)

Exam Fee

~$1,000 (Casualty Actuarial Society (CAS))

MAS-I Exam Content Outline

20%

Probability Models

Discrete and continuous distributions, moments, MGF, characteristic functions, mixture distributions, transformations, conditional expectation

20%

Stochastic Processes

Markov chains (transition matrices, classification, stationary distribution), Poisson processes (rate, inter-arrival times, thinning, superposition)

20%

Statistics & Estimation

MLE, method of moments, Fisher information, Cramér-Rao bound, asymptotic normality, invariance, unbiasedness, consistency, efficiency

15%

Confidence Intervals & Hypothesis Testing

CIs for means/proportions/variance, Type I/II errors, power, p-values, t-tests, F-tests, chi-square goodness-of-fit, contingency tables

15%

Linear Regression

OLS estimation, Gauss-Markov assumptions, residual diagnostics, R² and adjusted R², ANOVA, multicollinearity (VIF), leverage, Cook's distance

10%

Time Series Analysis

Stationarity (weak/strict), ACF/PACF, AR(p), MA(q), ARMA(p,q), ARIMA(p,d,q), unit root tests (ADF), Box-Jenkins methodology

How to Pass the MAS-I Exam

What You Need to Know

  • Passing score: Scaled (~6/10 typical)
  • Exam length: 45 questions
  • Time limit: 4 hours (CBT)
  • Exam fee: ~$1,000

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

MAS-I Study Tips from Top Performers

1Drill MLE problems until the score function and Fisher information setup is automatic — these appear in nearly every sitting
2Build muscle memory for Markov chain stationary distributions (πP=π) and Poisson process thinning/superposition; both are high-yield
3Practice OLS matrix algebra β̂ = (X'X)⁻¹X'y by hand on small examples before relying on calculator output
4Memorize ACF/PACF cutoff patterns for AR(p), MA(q), and ARMA(p,q) — pattern recognition saves time on every time-series question
5Use timed 45-question mocks at exam pace (~5.3 min/question) and track which categories burn the most clock

Frequently Asked Questions

How is the CAS MAS-I exam structured?

MAS-I is a 4-hour computer-based exam with approximately 45 multiple-choice questions delivered at Pearson VUE testing centers. The CAS administers MAS-I in two windows each year: Spring (April 22 - May 1 in 2026) and Fall (October 28 - November 5 in 2026). Results are reported on a 0-10 scale where any 6-10 score is a pass.

What is the MAS-I pass rate?

Recent CAS sittings show MAS-I pass rates of roughly 30-40%, making it one of the more challenging actuarial exams in the early ACAS pathway. The exam blends classical statistics with linear regression, time series, and stochastic process applications, so candidates who skip any single topic area struggle to clear the cut score.

How much does CAS Exam MAS-I cost?

The all-in cost for MAS-I runs approximately $1,000 once registration, syllabus material, and Pearson VUE testing-center fees are included. CAS publishes the official fee schedule on its website and adjusts pricing annually. Late registration windows generally add a surcharge, so registering during the standard window keeps total spend lower.

How long should I study for MAS-I?

Most successful MAS-I candidates report 300-500 hours of dedicated study. The exam assumes prior calculus, linear algebra, and intro probability (typically covered in CAS Exams 1 and 2), and the heavy linear-models and time-series content rewards working full problem sets rather than passive reading. Plan 3-5 months of consistent prep with timed practice sessions.

What topics carry the most weight on MAS-I?

Probability Models, Stochastic Processes, and Statistics & Estimation each carry roughly 20% of the exam. Confidence Intervals & Hypothesis Testing and Linear Regression sit at 15% each, and Time Series Analysis carries 10%. Together that means about 60% of the exam tests classical probability and inferential statistics, with the remaining 40% focused on regression and time-dependent modeling.

What credential does passing MAS-I count toward?

MAS-I is required for the Associate of the Casualty Actuarial Society (ACAS) credential. Candidates also need MAS-II, CAS Exams 5 and 6, the CAS online courses, and Validation by Educational Experience (VEE) credits in economics, accounting/finance, and mathematical statistics. MAS-I is typically taken after CAS Exams 1 and 2.