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5.2.12. Let the random variable Zn have a Poisson distribution with parameter μ = n. Show...

5.2.12. Let the random variable Zn have a Poisson distribution with parameter μ = n. Show that the limiting distribution of the random variable Yn =(Zn−n)/√n is normal with mean zero and variance 1.
(Hint: by using the CLT, first show Zn is the sum of a random sample of size n from a Poisson random variable with mean 1.)

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