Suppose that k ~ B(n,) where n is large and is small but n =
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Suppose that k ~ B(n,π) where n is large and π is small but nπ = λ has an intermediate value. Use the exponential limit ( 1 + x )^{n} → e^{x} to show that P(k = 0) ≌ e^{}^{λ }and P(k = I) ≌ λe^{}^{λ }. Extend this result to show that k is such that
that is, k is approximately distributed as a Poisson variable of mean λ.
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p(k)= exp(2) 2k k!
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Given k follows a binomial distribution with parameters n and such that n is large T is small and n ...View the full answer
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