INEQUALITIES FOR MULTINOMIAL ALLOCATIONS WITH APPLICATION TO DNA-FINGERPRINTING

We consider an allocation of n balls into N cells according to probabi lities pi. Assuming that the balls are allocated successively, denote by phi(n, N) the number of such balls which go into an already occupie d cell. If n = 2 the probability that two balls will occupy the same c ell is equal to the so-called match probability MP = p(1)(2) +...+ p(N )(2). An upper estimate for the probability P(phi(n, N) less than or e qual to m) which depends only on n and MP is derived. Such inequalitie s are important for estimation of the reliability of DNA fingerprintin g, a new method of crime investigation which is currently much debated .