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Question
Write the conditions for which the poisson distribution is a limiting case of binomial distribution
Solution
Poisson distribution is a limiting case of binomial distribution under the following conditions:
(i) n, the number of trials is indefinitely large i.e n → `∞`
(ii) p, the constant probability of success in each trial is very small, i.e. p → 0.
(iii) np = λ is finite.
Thus p = `lambda/"n"` and q = `1 - (lambda/"n")`
Where λ, is a positive real number.
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