Andy wrote: << So returning to the original question, the chance that the length of the left-hand piece is <= x is the chance that both points are >= x, which is (1-x)^2. So the answer to Dan's question is the value where (1-x)^2 = 1/2. So the best guess is 1 - (sqrt(2) / 2).
Which is the answer I had in mind. That didn't slow you down at all, Andy. But if I ever knew that the median minimizes expected absolute error, I had entirely forgotten, so also thanks to Andy for a nice explanation of why that's true -- and solves this problem a good deal faster than the way I used. Here's the discrete version of the puzzle, where I don't know if the median trick is helpful: ---------- Suppose two numbers are chosen from {1,2,3,...,52} without replacement, independently at random. What is the best real number guess G (in closed form) for the value of the smaller number, if once again best means having least expected absolute error in the long run? ---------- --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx