Suppose that X has a Poisson distribution with a very large mean Explain why the distribution of X can be approximated by the normal distribution with mean and variance In other words, explain why (X ) 1 2 converges in distribution, as , to a random variable having the standard normal distribution

Question: Suppose that X has a Poisson distribution with a very large mean . Explain why the distribution of X can be approximated by the normal

Suppose that X has a Poisson distribution with a very large mean λ. Explain why the distribution of X can be approximated by the normal distribution with mean λ and variance λ. In other words, explain why (X − λ)/λ1/2 converges in distribution, as λ→∞, to a random variable having the standard normal distribution.

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