If X has normal distribution, Y has normal distribution, X and Y are independent, but (X, Y) has no bivariate normal distribution.
This is false right?
Is it possible to obtain a counter example?
2026-03-30 20:54:10.1774904050
X and Y independent and has Normal distribution. Their Joint Distribution is a normal bivariate distribution.
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If they are independent and normal then $(X,Y)$ definitely has a bivariate normal distribution. You can write down the two dimensional normal density using that fact that$f_{X,Y} (x,y)=f_X(x)f_Y(y)$.