In a video lecture, MrProf shows the 3d-plot of a bivariate normal distribution $\mu_{x_1} = \mu_{x_2} = \sigma_1 = \sigma_2 = 1$ and chooses $\rho = 0.5$ .
If stick to Mathworld, $\rho$ simply is the Pearson correlation that is $\dfrac{\mbox{cov}(x_1, x_2) }{[ \mbox{var}(x_1) \mbox{var}(x_2)]^\frac{1}{2}}$.
I don't understand why one would have control over $\rho$ as in the example given by MrProf. I understood that $\rho$ is an output from the formula as I plug in $x_1$ and $x_2$, not an input.
Can anyone throw any light?