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It is assumed that a crystal structure in P1 is fixed and that the random variables (vectors) h, k, l, m, n are uniformly and independently distributed over the subset of reciprocal space defined by h + k + l + m + n = 0. Then the 15 structure factors Eh, Ek, El, Em, En, Eh + k, Eh + l, Eh + m, Eh + n, Ek + l, Ek + m, Ek + n, El + m, El + n, Em + n as functions of the primitive random variables h, k, l, m, n, are themselves random variables, and their joint probability distribution is found. This distribution plays the central role in the theory and estimation of the five-phase structure invariants φh + φk + φl + φm + φn.