Past exam of the mathematics course of the University of Cambridge / 2009 / ia / Paper 2 / 3F / a / Solution

With ${\sigma }_1,{\sigma }_2>0$ and $|\rho |<1$, the bivariate normal distribution has probability density functionThe strict correlation bound makes its covariance matrix positive definite, so this is an ordinary two-dimensional density rather than a distribution supported on a line.