<![CDATA[How can I plot a bivariate normal distribution in 3D to slice it to show conditional Expectation?]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation
Sun, 14 Feb 2021 21:51:30 +0000Sun, 14 Feb 2021 17:28:58 +0000Zend_Feed<![CDATA[φ(x, μ, σ) = 1 / sqrt(2π σ) ℯ^((-(x - μ)²) / (2σ²))
a(x, y) = φ(x, 0, 1) φ(y, 0, 1) ?]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298370
Sun, 14 Feb 2021 17:53:54 +0000<![CDATA[Thank you, but these would be independent Gaussians, I believe. The idea is to have some correlation between them.]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298372
Sun, 14 Feb 2021 18:11:13 +0000<![CDATA[then you have to give an example of what you are implying with "bivariate normal distribution"]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298374
Sun, 14 Feb 2021 18:50:48 +0000<![CDATA[I found the equations I needed to generate it with Geogebra, I think, and if I can only bring back up the CAS column to finish typing them in, I feel optimistic that I'll be able to share. However, there is I don't understand what you mean by 'implication' in "bivariate normal distribution - a quick search returns on MathWorld, for example, exactly what I am saying: https://mathworld.wolfram.c...]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298376
Sun, 14 Feb 2021 19:18:19 +0000<![CDATA[nothing wrong with that, the moment μ_{1}=μ_{2}=0 and σ_{1}=σ_{2}=1 , ρ=0 so it is the same for other cases you have to calculate ρ, if you know how to do that easily let me know i want to learn too φ(x, μ, σ) = 1 / sqrt(2π σ) ℯ^((-(x - μ)²) / (2σ²))
φ_{xy}(x, y, μ_{1}, μ_{2}, σ_{1}, σ_{2}, ρ) = 1 / (2π σ_{1} σ_{1} sqrt(1 - ρ²)) ℯ^((-((x - μ_{1})² / σ_{1}² - (2ρ (x - μ_{1}) (y - μ_{2})) / (σ_{1} σ_{2}) + (y - μ_{2})² / σ_{2}²)) / (2 (1 - ρ²)))
f(x, y) = φ(x, 0, 1) φ(y, 0, 1)
g(x, y) = φ_{xy}(x, y, 0, 0, 1, 1, 0)]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298380
Sun, 14 Feb 2021 19:52:11 +0000<![CDATA[Exactly. Here is my approximation, but I wish I could make the z values more apparent visually with a gradient of colors. https://www.geogebra.org/m/zrajyym7]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298386
Sun, 14 Feb 2021 20:49:09 +0000<![CDATA[Try with IntersectPath(b,p)
and line thickness higher ]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298390
Sun, 14 Feb 2021 20:22:49 +0000<![CDATA[I was actually trying exactly that - I am sure I learned it from you in the past. Thank you! Any way to do a color gradient for z values?]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298396
Sun, 14 Feb 2021 20:50:55 +0000<![CDATA[unfortunately GGb does not support shading of lines or surfaces (coloured gradients or value dependent colorization) (although it would be a very cool feature) the only option to achieve a similar effect is using trace paths with coded colour changes]]>
https://help.geogebra.org/topic/how-can-i-plot-a-bivariate-normal-distribution-in-3d-to-slice-it-to-show-conditional-expectation#comment-298400
Sun, 14 Feb 2021 21:51:30 +0000