In this problem, you may find it useful to recall the following fact about Poisson random variables. Let X and Y be two independent Poisson random variables, with means ? ₁ and ?2, respectively. Then, X + Y is a Poisson random variable with mean ? ₁ + ?2. Arguing in a similar way, a Poisson random variable X with parameter t, where t is a positive integer, can be thought of as sum of t independent Poisson random variables Xi , X2, ... , Xt, each of which has mean 1.

Using the information above, and an appropriate limit theorem, evaluate the following limit:

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lim n2-100 k>n+√n e-nnk k! lim n2-100 k>n+√n e-nnk k!

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Let X 1 X 2 X n be n independent and is identica... View the full answer