Which of the following describes the 'Law of Large Numbers' in the context of Monte Carlo simulations?
Question 2
When using Monte Carlo methods for numerical integration, if we want to estimate the integral of a function $f(x)$ over an interval $[a, b]$, and we sample $N$ points $x_i$ uniformly from this interval, what is the approximate value of the integral?
Question 3
Which of the following is a technique used for variance reduction in Monte Carlo simulations?
Question 4
In probabilistic modeling using Monte Carlo methods, what is the primary purpose of defining a 'probability distribution' for each input variable?
Question 5
Consider a Monte Carlo simulation for uncertainty quantification where the output variable $Y$ is a function of input variables $X_1, X_2, \dots, X_k$. If we run $N$ simulations, what does the collection of $N$ output values of $Y$ primarily provide?
Monte Carlo Methods Quiz — Applied Mathematics | A-Warded
