$Bivariate Normality questions$

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If both X and Y aren't normally distributed, would this mean they cannot bivariate normally?

I need any study online I can cite in order to prove these points. Thank you.

Multivariable Calculus Probability Statistics

Cocconut999

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Mathe

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Cocconut999

Is literally a small bounty for a small question. Not even asking you to solve a math problem or show me the demonstration.

Cocconut999

Is literally a small bounty for a small question. Not even asking you to solve a math problem or show me the demonstration.

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A fact about normal distributions:

Gaussian random vectors have several nice properties. One of the most important of these properties is that linear or affine operations on Gaussian random vectors produce Gaussian random vectors.

Robert M. Gray, Lee D. Davisson - An Introduction to Statistical Signal Processing-Cambridge University Press (2010)

Answer:
They can't be bivariate normal. If they were, the univariate projections $X = (1,0)\cdot (X,Y)$ and $Y = (0,1)\cdot (X,Y)$ would have a normal distribution.

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$Bivariate Normality questions$

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