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The expected length of the shorter piece

probabilityexpectationuniformsymmetry

A stick of length 1 is dropped and breaks at a single point chosen uniformly at random along its length.

What is the expected length of the shorter piece? And of the longer piece? Explain why the answer for the shorter piece is not one half, even though the average length of a piece is one half.

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The break point is a random number between 0 and 1. The shorter piece has length equal to the smaller of that number and one minus it. Draw its graph.

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