Product of independent uniform random variables

Carl P. Dettmann , Orestis Georgiou

We give an alternative proof of a useful formula for calculating the probability density function of the product of uniform, independently and identically distributed random variables. Ishihara (2002, in Japanese) proves the result by induction; here we use Fourier analysis and contour integral methods which provide a more intuitive explanation of how the convolution theorem acts in this case.

Mots clés: Physical Sciences

Carl P. Dettmann, Orestis Georgiou. Product of independent uniform random variables. Statistics and Probability Letters, 2009, 79 (24), pp.2501. ⟨10.1016/j.spl.2009.09.004⟩. ⟨hal-00589473⟩