Two points X1 and X2 are generated at random and independently from the Uniform[0,1] distribution. Let the smaller of the two points be X = min(X1, X2) and let the larger by Y = max(X1,X2). These two points X,Y are used to determine the break points in a rod of length 1 as in the figure below and this results in three pieces of length X, Y X and 1 - Y. Find the cumulative distribution function and the probability density function of the smallest of these three pieces, that is of the random variable W = min(X, Y X, 1 Y). Y 1