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Binomial Approximation to the Hypergeometric
Hypergeometrical distribution with parameters population size say ‘N’, number of trials say ‘n’ and number of successes say ‘K’ describes the number of successes one may possibly have in ‘n’ trials without any replacement from the population ‘N’. For example, from population ‘N’ of patients, a sample ‘n’ is drawn. Here number of patients with malaria in the population is assumed to be ‘K’. The distribution will help us to calculate the number of patients with malaria in the sample say ‘k’.
However, as we are sampling from a population which finite in nature without any replacement, so the result of these drawn samples will be dependent on the samples that have been drawn before them. But, if we come across a situation where the sample is very large and there will no effect on the population if a sample of size ‘n’ is removed from it. In such a situation, the probability of obtaining a sample with the characteristics which we are looking for will become constant and will be given by K/N. This is because; here the probability that the replaced item will be re-sampled again, is very less. Such cases where hypergeometrical distribution can be approximated by binomial distribution have been discussed in details by our experts of Binomial Approximation to the Hypergeometrical Assignment Help.
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