# Visualizing Conditional Gaussian

I am looking at a graph that depicts a conditional Gaussian:

I understand what the titled red spheres mean - that the variables are somewhat are correlated with each other.

I don't understand the significance of the blue line. I know it's related to conditional gaussian but I can't quite make sense of it.

Could someone explain what the blue line means?

Basically the bivariate normal distribution looks like this one:

Then the conditional distribution $$f_{Y|X=x}(x,y)$$ is here marked with the red line. We take the joint pdf and plug in $$x=1.6$$

$$f_{X,Y}(x,y) = \frac{1}{2 \pi \sigma_X \sigma_Y \sqrt{1-\rho^2}} \exp\left( -\frac{1}{2(1-\rho^2)}\left[ \frac{(x-\mu_X)^2}{\sigma_X^2} + \frac{(y-\mu_Y)^2}{\sigma_Y^2} - \frac{2\rho(x-\mu_X)(y-\mu_Y)}{\sigma_X \sigma_Y} \right] \right)$$

$$f_{Y|X=1.6}(1.6,y) = \frac{1}{2 \pi \sigma_X \sigma_Y \sqrt{1-\rho^2}} \exp\left( -\frac{1}{2(1-\rho^2)}\left[ \frac{(1.6-\mu_X)^2}{\sigma_X^2} + \frac{(y-\mu_Y)^2}{\sigma_Y^2} - \frac{2\rho(1.6-\mu_X)(y-\mu_Y)}{\sigma_X \sigma_Y} \right] \right)$$

This function does depend on the variable y only-the remaining unknowns are parameters. We can just draw the area at $$x=1.6$$ and omit all the other from the graph above. Then basically we get an univariate distribution of a normal distributed variable. At the graph below we see one example of $$f_{Y|X=x}(x,y)$$ and $$f_{Y|Y=y}(x,y)$$

Remark

The red circles (ellipses) at your graph show the different values of the joint distribution.