Abstract
Exact expressions are obtained for the moments of coverage of the random ellipsoid $$T_r (\bar x,S(X)) = \{ y|(y - \bar x)'S^{ - 1} (X)(y - \bar x) \leqq r\}$$ whereX=p1,...,p n is a sample from aN p (μ, Σ) distribution. This leads to approximations for the distribution of coverage and a solution to a problem in tolerance regions. An alternative expression is obtained for the distribution function of a quadratic form in normal variables.
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