# product variance

From a population characterised by variables ${\displaystyle x,\ y,\ z}$, correlated and normally distributed, with means ${\displaystyle 0,\ 0,\ 0}$, variances ${\displaystyle \sigma _{1}^{2},\ \sigma _{2}^{2},\ \sigma _{3}^{2}}$ and product variances ${\displaystyle r_{12}\sigma _{1}\sigma _{2},\ r_{13}\sigma _{1}\sigma _{3},\ r_{23}\sigma _{2}\sigma _{3}}$, a sub-population is extracted [] .