## Bivariate Validation

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For bivariate validation, 160,000 conditions were tested, consisting of 20 values each for $\mu_x$ and $\mu_y$ evenly distributed between 0 and 10, 20 values for $\sigma_x$ evenly distributed between 0.25 and 10, and 20 values for the ratio $\frac{\sigma_y}{\sigma_x}$ between 1 and 10. For each condition, 1,000,000 data were drawn from a bivariate normal distribution \$X \sim \mathcal{N}_2(\mu,\Si...