A.23 Bivariate normal distribution
The ordered pair (X, Y)T of observations has a bivariate normal distribution, denoted
if it has joint density
where
The means and variances are
and X and Y have correlation coefficient and covariance
Most properties follow from those of the ordinary, univariate and normal distribution. One point worth noting (which is clear from the form of the joint density function) is that if X and Y have a bivariate normal distribution, then they are independent if they are uncorrelated (a result which is not true in general).
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