The bivariate normal distribution's marginal distributions are univariate normal distributions.

Marginal normal distributions

If \((X,Y) \sim \NormalDistn(\mu_X, \sigma_X^2, \mu_Y, \sigma_Y^2, \rho)\) then the marginal distributions of \(X\) and \(Y\) are univariate normal,

\[ \begin{align} X \;\;&\sim\;\; \NormalDistn(\mu_X, \sigma_X^2) \\ Y \;\;&\sim\;\; \NormalDistn(\mu_Y, \sigma_Y^2) \end{align} \]

(Proved in full version)

From these, we can find the means and variances of the two variables.

Means and variances

If \((X,Y) \sim \NormalDistn(\mu_X, \sigma_X^2, \mu_Y, \sigma_Y^2, \rho)\) then

\[ \begin{align} E[X] \;&=\; \mu_X, \qquad &\Var(X) \;=\; \sigma_X^2 \\ E[Y] \;&=\; \mu_Y, \qquad &\Var(Y) \;=\; \sigma_Y^2 \end{align} \]