The parametric form considered for the Binomial Distribution has mean value kp and variance kp (l + p), where k, p > 0. The first order covariances of k, p, the maximum likelihood estimators of k and p respectively, are given as elements in the inverse of the covariance matrix. These covariances are asymptotic expressions in the sample size n and are only valid in so-called large sample theory. To determine in a rough way how large n must be for the first order covariances to be approximately correct, the second order terms have been evaluated and tabulated. From these an indication of the sample size needed to place some confidence in the traditional asymptotic formulae is worked out. The results show that very large sample sizes may be required when k and p are both small. A similar study of another commonly used parametrization is given.
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