Monte Carlo (Applied Mathematics) trivia

Monte Carlo (Applied Mathematics) Mini Quiz

Test your knowledge with these top questions!

Question 1

Classic Monte Carlo estimates of π sample points inside a circle and its surrounding what?

The circle-to-square area ratio lets point counts approximate π without measuring the circumference.

Question 2

Monte Carlo integration estimates an integral by averaging sampled values of what?

For uniform samples, scaling the mean integrand value by the domain size estimates the integral.

Question 3

Why does a Monte Carlo estimate usually become more stable with more independent samples?

The law of large numbers makes sample averages converge toward the expected value as independent samples accumulate.

Question 4

In Monte Carlo Metropolis sampling, what can happen when a proposed move lowers the target probability?

Accepting some lower-probability moves helps the chain explore the target distribution instead of becoming trapped.