  We extend a result of Goldreich and Ron about estimating the collision
probability of a hash function. Their estimate has a polynomial tail. We prove
that when the load factor is greater than a certain constant, the estimator has
a gaussian tail. As an application we find an estimate of an upper bound for
the average search time in hashing with chaining, for a particular user (we
allow the overall key distribution to be different from the key distribution of
a particular user). The estimator has a gaussian tail.
