Project ForgeDiscrete Mathematics
Probability & Combinatorics
GATE 2014
Medium
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is
0.25(± 0.02 accepted)
Explanation
Let X be uniform on [0,1], the break point. The shorter piece has length min(X, 1−X). By symmetry, E[min(X,1−X)] = 2·∫₀^0.5 x dx = 2·[x²/2]₀^0.5 = 2·(0.125) = 0.25.
Source: GATE CS 2014 (Session 1) (2014)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.