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**iaarzda** not really good with probability, any help would be appreciated.

A company manufactures metal poles. Suppose the length of a pole is a random variable X,with mean μX and probability density function fX(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 will be cut down to L, and the section left over is lost (even if it is big enough to cut a second pole). We are interested in the random variable Y,defined as the length of each piece lost.

(a) Sketch the graph of of the function g that maps the pole length x to the lost length y, and so derive μY \equiv E[Y ] as a function of fX(x) and μX.