Summen von Produkten gemeinsam normalverteilter Zufallsvariablen

Summary

For an arbitrary 2n-dimensional centered multivariate normal random vectorX=(X ₁, ...,X _2n ) the distribution of$Z: = \mathop \sum \limits_{i = 1}^n X_i X_{n + 1}$ is computed. It turns out to be a convolution of a collection ofx ²₁ -distributions with scale parameters depending on the covariance matrix ofX. Forn=1, the case of the bivariate normal distribution, the characteristic function ofZ is explicitly given also in the case of non-centeredX.