### Smallest Number in Decreasing Sequence

Source: Quantnet Forums Problem: You pick random numbers between 0 and 1 (uniformly at random) x1, x2, x3.. as long as they keep decreasing x1 > x2 > x3 > ... What is the expected value of the smallest number you pick? Update (26-05-2011): Solution: Posted by Gaurav Sinha (chera, IITK 1996 Graduate, Indian Revenue Service) in comments! Interesting approach (although wrong) by Gautam Kamath (EE, Senior Undergraduate, IIT Bombay) in comments - Corrected by me!