The Bivariate Normal and Conditional Distributions

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If is a normal random variable and the conditional distribution of
given
is (1) normal, (2) has a mean that is a linear function of
, and (3) has a variance that is constant (does not depend on
), then the pair
follows a bivariate normal distribution. The left image is a graph of the bivariate density function and the right image shows the conditional distribution of
when
takes the value of the
slider.
Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA
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"The Bivariate Normal and Conditional Distributions"
http://demonstrations.wolfram.com/TheBivariateNormalAndConditionalDistributions/
Wolfram Demonstrations Project
Published: March 7 2011