A Winner's Mean Earnings in Lottery and Inverse Moments of the Binomial Distribution

الملخص EN

We study the mean earnings of a lottery winner as a function of the number n of participants in the lottery and of the success probability p.

We show, in particular, that, for fixed p, there exists an optimal value of n where the mean earnings are maximized.

We also establish a relation with the inverse moments of a binomial distribution and suggest new formulas (exact and approximate) for them.