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Random walks of 100 steps or less in a three‐dimensional tetrahedral lattice have been generated by means of the ILLIAC computer. Excluded volume has been introduced by forbidding double occupancy of lattice sites. The distribution function of end‐to‐end lengths has been collected and expanded in terms of Hermite polynomials. One finds that the distribution can be expressed as a two‐term expansion, the second term contributing 10% at 100 steps. For walks of a given number of steps and a given end‐to‐end length the spatial distribution of monomer segments has been investigated and compared to the (no excluded volume) expression of James. One finds that the introduction of excluded volume swells the chains and increases the moment of inertia along the major axis.

A nonparametric relation is derived between the discrete probability distribution (pi, ci}, assumed for toxin concentration c in individual members of a population, and the probability distribution {Pi(n)} of the toxin concentration in n-member samples taken from that population. Here pi is the probability of an individual member having toxin concentration ci, while Pi(n) is the probability of an n-sample exhibiting toxin concentration falling in range i of C. An information theoretic basis is given for the number J of indices i required for {Pi(n)}. The same number of indices is used for (pi, ci}; additional values, if needed, are estimated. {Pi(n)} is derived from (pi, ci} by multinomial Poisson statistics. Conversely, it is shown how (pi, ci} may be derived from empirical {Pi(n)} data when the npi are small, as is commonly the case for aflatoxin contamination of tree nuts. As a first approximation one obtains pi = Pi(n)fn and Ci = n * Ci, where Ci is the midpoint of range i of C.Higher approximations are evaluated as well. A basis is thus laid for computing {Pi(n)} for a sample size differing from that of the sample actually determined. The results are applied to predicting . the probability of a sample of any size exceeding a predetermined level C,.

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