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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?

sandra
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  • Variables follow bivariate normal distribution if they follow [bivariate normal distribution](https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Bivariate_case). It is not about having two normally distributed variables, but also about their joint distribution. – Tim Feb 13 '20 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.

Earlien
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