A new proof that the product of three or more exponential random variables is moment-indeterminate

We present a direct, short and transparent proof of the following result: The product X1⋯XnX1⋯Xn of independent exponential random variables X1,…,XnX1,…,Xn is moment-indeterminate if and only if n≥3n≥3. This and other complex analytic results concerning Stieltjes moment sequences and properties of the corresponding distributions appeared recently in Berg (2005).