GATE 2014 CS (CS1) – Question 12
A unit-length stick is broken at a point chosen uniformly at random. Find the expected length of the shorter stick.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.24 to 0.27
Explanation
If the cut position X is uniform on[0,1], the shorter length is min(X,1−X). Symmetry gives expectation2∫₀^(1/2)x dx=2×1/8=**0.25**. The shorter segment never exceeds1/2, unlike the unrestricted cut location.