The Bivariate Normal Distribution

μ

x

0

μ

y

0

σ

x

1

σ

y

1

ρ

0.

The bivariate normal distribution is a distribution of a pair of variables whose conditional distributions are normal and that satisfy certain other technical conditions. The density function is a generalization of the familiar bell curve and graphs in three dimensions as a sort of bell-shaped hump. The parameters

μ

X

and

μ

Y

are the means of the coordinate variables

X

and

Y

, the parameters

σ

X

and

σ

Y

are their standard deviations, and the parameter

ρ

is the correlation between them.