THE 123 THEOREM AND ITS EXTENSIONS

[摘要] It is shown that for every b > a > 0 and for every two independent identically distributed real random variables X and Y, Prob[\X - Y\ less than or equal to b] < (2[b/a] - 1) Prob[\X - Y\ less than or equal to a]. This is tight for all admissible pairs a, b. Higher dimensional extensions are also considered. (C) 1995 Academic Press, Inc.

[发布日期] 1995-11-01