Suppose that k ~ B(n,) where n is large and is small but n =


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 → ex to show that P(k = 0) ≌ e-λ and P(k = I) ≌  λe-λ . Extend this result to show that k is such that 

p(k)= exp(-) 2k k!

that is, k is approximately distributed as a Poisson variable of mean λ.

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