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Products of Random Numbers

Summary In this article the probability distribution of a product of independent random numbers is derived in an elementary way by considering a truncation problem. A random number is defined to be a random variable uniformly distributed in the interval [0,1]. Let F n (x) be the probability that a product of n random numbers does not exceed x. A direct and elementary proof is given for the formula Fn(x) = x‐en(‐logx) (1) where the polynomial function en(.), a truncated e‐function, is defined by The relation of (1) to the gamma distribution is discussed. It is also shown that the expected minimal number of random factors in a product not exceeding x is 1‐log x