CAS Modern Actuarial Statistics II Practice Test
Modern actuarial statistics applies statistical modeling and inference to insurance data and uncertainty. This MAS-II practice bank samples concepts such as finite mixture models, decision-tree overfitting, log-scale predictions, causal effects, credibility estimates, quantile regression, and expected shortfall. Questions also address hypothesis tests, analysis of variance, and the gap between training and validation loss.
Exam overview
About the CAS Modern Actuarial Statistics II Exam
The questions exercise interpretation as well as computation: identify constraints on mixture probabilities, distinguish a conditional quantile from a mean, and translate a fitted log response back to its original scale. Other items test how credibility blends group experience with a collective estimate, how potential outcomes define an average treatment effect, and how expected shortfall summarizes losses beyond a value-at-risk threshold. Testing scenarios include interpreting a p-value against a stated significance level and recognizing what a standard ANOVA F-test evaluates. Predictive-model questions connect tree depth and the difference between training and validation loss to generalization on new data. These skills support actuarial work that involves selecting and assessing statistical methods, interpreting model output, and communicating uncertainty in claim and risk estimates.
Sample Practice Questions
Review a selection from this exam's published US Practice Tests practice bank.
In a two-component finite mixture model, an observation is generated by first selecting component k with probability π_k and then drawing from that component's distribution. What constraint must the mixing probabilities satisfy?
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Correct answer: BThe mixing probabilities describe mutually exclusive component membership and therefore form a probability distribution: each is nonnegative and their sum is one.
A decision tree is grown to very great depth without pruning. Which behavior is most likely when it is evaluated on new data?
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Correct answer: AA very deep tree can capture idiosyncrasies and noise in the training sample, producing low training error but high variance. Pruning, depth limits, or other regularization can help control this overfitting and improve generalization.
A fitted model gives a log predicted claim amount of 2.0, and the response was modeled on the natural-log scale. What is the direct back-transformation of this fitted value to the original scale?
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Correct answer: CThe inverse of the natural logarithm is the exponential function, so the direct back-transformation is exp(2.0). This is a back-transformed fitted log-scale value; it is not necessarily the conditional mean on the original scale when residual variation is present.
In a randomized experiment, a researcher wants to estimate the average causal effect of treatment assignment using potential outcomes. Which quantity is the average treatment effect?
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Correct answer: AThe average treatment effect is the population average of each unit's treatment potential outcome minus its control potential outcome. Random assignment supports estimating this contrast because assignment is independent of the potential outcomes, subject to the design and analysis assumptions.
A credibility estimate is Z times the observed group mean plus (1 − Z) times the collective mean. If Z = 0, which estimate results?
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Correct answer: BSubstituting Z = 0 leaves 0 times the observed mean plus 1 times the collective mean, so the estimate is fully based on the collective mean.
In a standard quantile regression model, what feature of the conditional response distribution does the fitted value at quantile level τ target?
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Correct answer: BQuantile regression models a specified conditional quantile, such as the conditional median when τ = 0.5. It need not model the conditional mean.
For a continuous loss X with finite mean, which quantity is the expected shortfall at confidence level α, using the convention ESα = E[X | X ≥ VaRα] when the threshold has no point mass?
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Correct answer: AUnder the stated continuous-loss convention, expected shortfall is the conditional average loss in the tail at or beyond the value-at-risk threshold. It measures tail severity, whereas VaR itself is a quantile.
How to use this practice test
Access is free. A session presents up to 20 random questions from the 50-question practice bank and shows results afterward. Use the questions to pinpoint which statistical interpretations or calculations need another pass; results reflect this practice session, not a formal exam outcome.
Preparation tips
- For finite mixtures, write the nonnegativity and sum-to-one constraints for component probabilities before interpreting a model.
- Practice converting log-scale predictions back to the original response scale, and distinguish a direct transformation from any bias adjustment.
- Compare credibility estimates at Z = 0 and Z = 1 to check how group experience and the collective mean contribute.
- For quantile regression and expected shortfall, state the target quantity and confidence or quantile level before applying the definition.
- Explain what each test evaluates: the ANOVA overall F-test, a p-value decision at a chosen significance level, and validation loss as evidence about generalization.