Hi! I am a new member, and I'm posting b/c I have a question from the practice list I have received as a practice for an upcoming quiz. I've done many questions where mass x (or y) is dependent of x. However, I've come across one where the length of a piece x (of two) is completely independent of x: Suppose you have a stick of length L that you would like to cut into two pieces. Assume that the cutting is completely random, that the (1) probability density p(x) for having either one of the pieces be of mass x is completely independent of x. Find the function p(x). So, I did integral (from x =0 to x=L) p(x)dx = integral (x=0 to x = L) C dx = 1 for normalization. (I put C as a constant). Then, I equivelated 1 = C integral (x=0 to x = L) dx = C x/(x=0 to x = L) which becomes: 1 = C (L - 0) = CL C = 1/L ...and, from this, how am I to get the function p(x)? Do I just put p(x) = 1/L? Also, in case I want to find the (2) average length of one piece (preferably a larger one? w/out L/2 value), how do I solve it? For this, I did the similar thing as above, except: integral (from y = L/2 to L) p(y) dy = integral (y = L/2 to L) C_new dy = 1 for normalization (I put y = larger piece) THen I equivalted 1 = C_new integral (y = L/2 to L) dy 1 = C_new (L - L/2) 1 = C_new (L/2) C_new = 2/L.... So, I wonder if average is 2/L, from 2/L integral (y=L/2 to L) y*dy? Or, is it L/2? Any suggestions or replies would be welcome!