Showcase of importance sampling. The upper panel shows a histogram of 2000 samples directly sampled from a Maxwell-Boltzmann probability density distribution, f(x). In the lower panel, the same amount of samples are sampled from a Gaussian probability density distribution, g(x), which is shifted towards higher x values compared to the Maxwell-Boltzmann distribution. This shift increases the fraction of samples with high x-values compared to the direct sampling, and if the samples are weighted with the ratio f(x)/g(x) when binned, the resulting histogram will estimate the Maxwellian-probability distribution, but this time with higher statistical accuracy for the higher values of x.