, i.e., X As a by-product, we derive the exact distribution of the mean of the product of correlated normal random variables. z Thus, in cases where a simple result can be found in the list of convolutions of probability distributions, where the distributions to be convolved are those of the logarithms of the components of the product, the result might be transformed to provide the distribution of the product. {\displaystyle f_{Z_{n}}(z)={\frac {(-\log z)^{n-1}}{(n-1)!\;\;\;}},\;\;0