Three question related to stick breaking. A stick is of length 1.
1) The stick drops and breaks at a random point distributed uniformly across the length. What is the expected length of the smaller part? (Source: DB interview)
2) In the above experiment, what is the expected length of the larger part? (Source: Made it up)
3) In the third experiment, the stick is dropped and breaks at two points. What is the probability that the three pieces could form a triangle? (Source: V.K.Bansal notes, MathOverflow.net)
Update (18/12/09): Solution: Partial solution by Aaditya Ramdas (CSE IITB 2005-2009) and Giridhar Addepalli (CSE, IITK alumnus and Yahoo! Sr. Software Engineer) and complete solution by me in comments.