aez-notes

(a) If a stick is broken in two at random, what is the average length of the smaller piece? (b) (For calculus students.) What is the average ratio of the smaller length to the larger?

The shorter one has a length uniformly distributed from 0 to 1/2 hence the solution is 1/4. For the second part we evaulate the integral.

print(float(integrate( (x / (1-x)) * 2, x, 0, 1/2 )));
/*
0.3862943611198906
*/