The Meaning of Binamial Distribution
Journal/Book: (Reprinted from Natura Vol. 186 No. 4730 p. 1074 only June 25 1960). 1960;
Abstract: Department of Genetics University of Cambridge. Feb. 12. Two generalizations of the simple binomial distribution are common in statistical text-books one due to W. Lexis and the other to S. D. Poisson. Lexis considered the case in which the probability of an event occurring p is constant in the N trials of one experiment but varies among several such experiments. He showed that the mean and variance of the resulting binomial distribution are Np and Npq + N(N-1)V(p) where p= 1-q is the mean and V(p) the variance of p between experiments. The variance thus exceeds that of the simple binomial distribution with the same mean. Poisson considered the case in which p takes the value pi at the ith trial in each experiment and showed that the mean and variance of the resulting distribution are Np and Npq - NV'(p) where V'(p) is the variance of p within experiments. . . .