Gelman and Meng XXXXXXXXXXgive an an example of a bivariate family of distributions that are not...

Question

Gelman and Meng XXXXXXXXXXgive an an example of a bivariate family of distributions that are not bivariate normal but have normal conditionals. Define the joint pdf of (X, Y) as
where A, B, C, D are constant.
(b) A most interesting configuration is A = 1, B = 0, C = D = 8. Show that this joint distribution is bimodal.
*the solution uploaded on the site is wrong.

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Monica · Accepted Answer

Solution 
Bimodal Distribution 
A bimodal distribution is a probability distribution with two modes.
Given:
Gelman and Meng (1991) give an example of a bivariate family of distribution 
where, A = 1, B = 0, C = 8,

Gelman and Meng XXXXXXXXXXgive an an example of a bivariate family of distributions that are not bivariate normal but have normal conditionals. Define the joint pdf of (X, Y) as where A, B, C, D are...

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