Example of correlated Monte Carlo samples. Top panel: strengths of our three example resonances including their uncertainties. Middle panel: uncorrelated (blue – y_j) and correlated (grey – ) normally distributed samples, which are used to compute the resonance strengths in Eq. (17). Note that after applying the correlation outlined in the text, resonances 2 and r become highly correlated whereas resonance one remains largely unchanged. Lower two panels: density distributions of the samples, and confirms that the individual distributions do not vary outside of statistical fluctuations.