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$\newcommand{\Var}{\operatorname{Var}}\newcommand{\Cov}{\operatorname{Cov}}$Could you help me to check that for every Gaussian vector $(Z_1,Z_2,\ldots, Z_n)$, we have $\det\Cov(Z_1,\ldots, Z_n)$ $= \Var Z_1 \Var (Z_2/Z_1) \Var(Z_3/Z_1,Z_2)\cdots\Var(Z_n/Z_1,\ldots,Z_{n-1})$

Thank you in advance

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Gladly--if only you explain what you tried to solve this (and how the LHS (a number) can equal the RHS (a random variable)). –  Did Jun 1 '13 at 16:44

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