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Adding local short description: "Probability theory and statistics concept", overriding Wikidata description "probability distribution restricted to a subspace of the sample space, normalize to a total probability of one" |
Change the indexes of the example expression. The expression had presumably been copied from some other place using X_1 and X_2 instead of X and Y so there was a bit of a confusing mismatch where it was not clear whether mu_1 relates to X or Y |
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The graph shows a [[bivariate normal distribution|bivariate normal joint density]] for random variables <math>X</math> and <math>Y</math>. To see the distribution of <math>Y</math> conditional on <math>X=70</math>, one can first visualize the line <math>X=70</math> in the <math>X,Y</math> [[plane (geometry)|plane]], and then visualize the plane containing that line and perpendicular to the <math>X,Y</math> plane. The intersection of that plane with the joint normal density, once rescaled to give unit area under the intersection, is the relevant conditional density of <math>Y</math>.
<math>Y\mid X=70 \ \sim\ \mathcal{N}\left(\
==Relation to independence==
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