Free CAS MAS-II (Modern Actuarial Statistics II) Practice Questions

B is correct. A moving-average MA(q) process expresses $Y_t$ as a finite linear combination of the contemporaneous innovation $\epsilon_t$ and its q most recent lags. Because no lagged values of the series itself appear on the right-hand side, MA(q) processes are always weakly stationary for any choice of MA coefficients.

E is correct. Bagging averages predictions from trees fit to bootstrap samples, which by itself only modestly reduces variance because the trees remain highly correlated. The trees tend to share top-level splits on the same dominant predictors. Random forests restrict each split to a random subset of predictors, which forces the trees to diverge and lowers the pairwise correlation between them. Because the variance of an average of correlated predictors depends on that correlation, the decorrelation step lowers ensemble variance below what bagging achieves.

E is correct. Bayesian and Buhlmann credibility coincide exactly when the Bayesian posterior mean is itself a linear function of the observed mean. This linearity arises in the standard conjugate exponential-family models, of which the Poisson likelihood with a Gamma prior is the canonical example. Other conjugate combinations with the same exact-linearity property include Normal/Normal, Bernoulli/Beta, and Exponential/Gamma. In each, the posterior mean can be written as a credibility-weighted average of the prior mean and the observed mean with weights matching the Buhlmann formula. The non-conjugate pairings listed elsewhere lack this closed-form linear posterior, so Buhlmann is only an approximation rather than an exact match.