| [ QuizWit ] in KIDS 글 쓴 이(By): guest (OTiS) 날 짜 (Date): 1998년02월19일(목) 04시49분43초 ROK 제 목(Title): Yut Chi-Gi Problem. The following problem is very famous statistical problem. Similar problem in 3-dim. was also proposed in Putnam. Problem: There is a string of length 1. Cut the string into n substrings. Assume that the postion we cut ( n-1 cutting to have n substrings.) is random. ( uniformly distributed.) Find the expected length of the largest substring. Hard Problem: Find the joint density of the lengths of n substrings. The answer is trivially simple!!!!!! Hint: Problem can be viewed as n-dimensional perpendicular simplex. The volume of such simplex has factor n! :) |