Past exam of the simulation and statistical programming course of the University of Oxford / 2023 / 1 / a / ii / Solution

Apply Chebyshev's inequality to the Monte Carlo estimator:Thus $10^4/n\le 0.01$ suffices, givingThis is a finite-sample probability guarantee for every target satisfying the given variance assumption. It is a sufficient sample count supplied by the inequality, rather than a claim that every such target actually needs a million draws.