The distribution of random segment lengths

Choice of the correct distribution of sediment thicknesses is necessary in studying reflection of acoustic rays from randomly layered sediments and in many seismic applications. We consider a set of N segment lengths, {1_i}, i=1, 2, 3,..., N, whose combined length is L. Three cases are of interest: 1) L and N are known constants, 2) the number of segments N is a known constant but L is a random variable with given expectation value <L>, and 3) both N and L are random variables with given expectation values <N> and <L>, respectively. The distribution of segments lengths is calculated for each of the three cases under the assumption that any set {1_i} is as probable as any other set fulfilling the same conditions. The expressions are simple and easy to implement.