Apr 11, 2011

Smallest Number in Decreasing Sequence

Source: Quantnet Forums

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!

Fraction Brainteaser

Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20...