A Winner’s Mean Earnings in Lottery and Inverse Moments of the Binomial Distribution
نویسندگان
چکیده
The game of lottery is both popular and simple. Focusing on the essentials, and leaving aside additional features of secondary importance, which vary across different lottery implementations, the rules of the game are as follows: each player submits to the lottery organizers a ticket consisting of M integers selected by the player, without repetitions, selection order being unimportant from the range 1, . . . ,N; within the prespecified time period the game is set to last; upon the expiry of this period no more ticket submissions are accepted, and an M-tuple of distinct integers the “winning set” is selected uniformly at random by the lottery organizers; each submitted ticket gets compared against the winning set, and, if they match, the corresponding player “wins.” This is known as an M/N lottery system, and the winning probability is clearly p 1/ ( N
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