Free SOA Exam SRM (Statistics for Risk Modeling) Practice Questions

The key innovation of random forests over bagging is the random selection of a subset of $m_{try}$ predictors at each split point. This prevents dominant predictors from being used in every tree, thereby reducing the correlation between trees. Since the variance of an average of correlated quantities depends on the correlation, decorrelation leads to greater variance reduction.

Choice A is incorrect because both methods typically use full-depth trees.
Choice E is incorrect because both can use the same splitting criteria.
Choice B is incorrect because random forests, like bagging, fit trees independently (not sequentially -- that describes boosting).
Choice C is incorrect because both use standard bootstrap samples of size $n$.

The process $Y_t = 5 + 0.7Y_{t-1} + \epsilon_t$ is an AR(1) process with $\phi_1 = 0.7$. Since $|\phi_1| = 0.7 < 1$, this process is stationary. Its mean is $\mu = 5/(1 - 0.7) = 16.67$ and its variance is $\sigma^2/(1 - 0.7^2)$, both constant over time.

(B) is incorrect because the term $0.5t$ is a deterministic linear trend, causing the mean to increase with time.
(C) is incorrect because a random walk is non-stationary; its variance $t\sigma^2$ grows without bound.
(A) is incorrect because $\text{Var}(Y_t) = t^2 \sigma^2$ increases with time.
(E) is incorrect because the quadratic trend $10 + 2t + 0.3t^2$ causes the mean to change over time.

Ln(8500) +/- 1.96*0.15 => exp => (6370, 11340). PI: Gamma(5,1700) quantiles => (3200, 22560).

Choice C is incorrect because it uses the wrong shape parameter alpha=2 instead of 5 for the PI.
Choice B is incorrect because the PI is constructible using the gamma distribution with known shape.
Choice D is incorrect because the CI is too narrow from a normal approximation on the original scale.
Choice E is incorrect because it reverses the CI and PI widths.