You have a straight, 100cm length of vine, with thorns at each centimeter, from 0 to 100 inclusive. You dip it into liquid nitrogen and drop it. It breaks exactly halfway between two adjacent thorns, where the point of breakage is equally likely to be in between any pair of adjacent thorns. One piece must be longer than the other piece, since it couldn't have broken exactly at the middle thorn; call the shorter piece S and the longer piece L.

a. What's the expected number of thorns on S? To make this clearer, if we were talking about a length of vine with ten evenly spaced thorns on it and it broke between thorns 7 and 8, there would be 7 thorns on the longer piece, and the remaining three thorns would be on the shorter piece.

 b. What about the expected number of thorns on L? c. What is the expected value of the product of the number of thorns on S and the number of thorns on L?