Sticks

gardener3 · April 7th, 2006, 2:19 am

Consider the following bet:There are a number of sticks that are unit in length. We randomly select a point to break the sticks into two pieces. We repeat this for alrge number of sticks, say, 10,000. We then calculate the ratio of the long piece to the short one. What would you bet that the average ratio will be?

aym · April 7th, 2006, 3:03 am

2 log(2) - 1 (twice the integral of (1/2-a)/(1/2+a) between 0 & 1/2, 1/2-a is the length of the short side...) Edit: I misunderstood the question. I went for the ratio of the short to the long side...

actuaryalfred · April 7th, 2006, 3:03 am

Greater than 1. The expectation doesn't exist...

gardener3 · April 7th, 2006, 3:24 am

QuoteOriginally posted by: actuaryalfredGreater than 1. The expectation doesn't exist...Careful, only the arithmetic mean does not exist. Let me rephrase, suppose you were forced to provide an answer, what would be your best guess? would it be infinity?

mensa0 · April 7th, 2006, 6:03 am

See the discussion here:LinkMike

gardener3 · April 7th, 2006, 3:48 pm

Thanks for the link. I am surprised no one mentioned using harmonic or geometric mean to get at the solution. Both exist for this problem.

sevvost · April 7th, 2006, 8:59 pm

More links: the Line Point Picking page; another paper on the subject.