Suppose the length of a pole is a random variable X, with mean m(x) and probability density function f(x). Poles are cut to obtain an exact length L. If the initial length of the pole is less than L, the entire pole is lost. If it is greater than L, the pole with be cut down to L, and the section left over is lost. We are interested in the random variable Y, defined as the length of each piece lost. i) Sketch the graph y (values of Y) as a function of x (values of X), and derive m(y) = E[Y] as a function of f(x) and m(x). The graph... y=x , x < L y=x-L , x => L but how do I derive the mean of Y? Any helps as always greatly appreciated.