  For a sample of absolutely bounded i.i.d. random variables with a continuous
density the cumulative distribution function of the sample variance is
represented by a univariate integral over a Fourier series. If the density is a
polynomial or a trigonometrical polynomial the coefficients of this series are
simple finite terms containing only the error function, the exponential
function and powers. In more general cases - e.g. for all beta densities - the
coefficients are given by some series expansions. The method is generalized to
positive semi-definite quadratic forms of bounded independent but not
necessarily identically distributed random variables if the form matrix differs
from a diagonal matrix D > 0 only by a matrix of rank 1
