  From a suitable integral representation of the Laplace transform of a
positive semi-definite quadratic form of independent real random variables with
not necessarily identical densities a univariate integral representation is
derived for the cumulative distribution function of the sample variance of
i.i.d. random variables with a gamma density, supplementing former formulas of
the author. Furthermore, from the above Laplace transform Fourier series are
obtained for the density and the distribution function of the sample variance
of i.i.d. random variables with a uniform distribution. This distribution can
be applied e.g. to a statistical test for a scale parameter.
