A rubber band at temperature T is fastened at one end to a peg, and supports from its other end a mass m in a gravitational field g. Model the rubber band as a linked polymer chain of N segments joined end-to-end. Each segment has a length a and can be oriented either parallel or anti-parallel to the vertical direction. Find an expression for the average length of the rubber band as a function of B, m, g, N, and a. You may neglect the kinetic energies and masses of the segments themselves, and any interaction between the segments.

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