I wrote: << PUZZLE ------ Given real-valued random variables X,Y,Z in a joint distribution, suppose that the correlation coefficient* between any two of them is the same number C. QUESTION: What is the minimum value, over all such joint distributions, that C can take? (We assume all means and variances are finite.)
Gene and Veit found the lowest possible value, -1/2. (How Gene came up with his streamlined reasoning, I may never know.) Here is a related puzzle, hot off the press: PUZZLE: Let (x,y,z) be chosen at random from the uniform distribution on [-1,1]^3. If you guess that (x,y,z) actually forms a triple of correlation coefficients from 3 jointly distributed real random variables, are you more likely to be right or to be wrong? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele