4. Computational Modeling

Stochastic Models — Quiz

Test your understanding of stochastic models with 5 practice questions.

Practice Questions

Question 1

In importance sampling for estimating $I=E_f[h(X)]$, the proposal density $g^*(x)$ that minimizes the variance of the weighted estimator is proportional to which of the following?

Question 2

To achieve a 95\\% confidence interval half-width of $0.005$ for a Monte Carlo estimator with known standard deviation $\sigma=2$, how many independent samples $N$ are required (using $z_{0.975}=1.96$)?

Question 3

Using the Milstein method, the update for geometric Brownian motion $dX=\mu X\,dt+\sigma X\,dW$ is given by which expression?

Question 4

The Kolmogorov backward equation for the function $u(x,t)=E[\phi(X_T)\mid X_t=x]$ governed by the SDE $dX=a(x)\,dt+b(x)\,dW(t)$ is which of the following PDEs?

Question 5

In second-order uncertainty propagation for a scalar function $y=f(x)$ with $E[x]=\mu$ and $\mathrm{Var}(x)=\sigma^2$, the approximation for $E[y]$ includes which additional term beyond $f(\mu)$?