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Does bivariate normal distribution mean the two random variables have normal distributions? is that enough for two random variables to have a bivariate normal distribution or are there some other conditions that must be true?

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  • $\begingroup$ Variables follow bivariate normal distribution if they follow bivariate normal distribution. It is not about having two normally distributed variables, but also about their joint distribution. $\endgroup$ – Tim Feb 13 at 22:09
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A bivariate Normal distribution is a special cause of the multivariate Normal distribution in which the dimension is 2. It describes a single random variable, not 2 random variables

However, 2 independent univariate Normal random variables can be expressed as a special case of the bivariate Normal random variable with a diagonal covariance matrix (zeros of the off-diagonal).

Have a look at the second figure in this article for a visual explanation of the bivariate Normal distribution and its two corresponding marginal distributions which are univariate Normal.

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