Comments On "Testing a Sample Population for the Rayleigh Distribution" and a Succeeding Correction

In a recent correction [2] to previous correspondence [1] it was stated that 3) of the theorem in [1] was invalid due to the statistical dependence of the y
i
. The joint distribution function of the y
i
is derived below confirming their dependence, but also upholding the validity of Item 3. Furthermore, an exact goodness of fit test for the Rayleigh distribution based upon the
N + 1
observations
x_{1}, ... , x_{N+1}
is suggested.