Let Yn be a binomial random variable with n trials and
Chapter 7, Problem 104SE(choose chapter or problem)
Let \(Y_{n}\) be a binomial random variable with \(n\) trials and with success probability \(p\). Suppose that \(n\) tends to infinity and \(p\) tends to zero in such a way that \(n p\) remains fixed at \(n p=\lambda\). Use the result in Theorem 7.5 to prove that the distribution of 𝑌n converges to a Poisson distribution with mean \(\lambda\).
Equation Transcription:
Text Transcription:
Yn
n
p
n
p
Np
np=\lambda
\lambda
Yn
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