Let X be a binomial random variable with parameters n and p

Let X be a binomial random variable with parameters n and p = a/n. Using probability generating functions, show that, with a and k fixed, as n infinity Pr[X = k] e-G Gk/k! A text file containing 1000 characters is sent by email from one computer to another. It is known that each character (independently of all other characters) has probability 0.001 of being corrupted. Use a poisson random variable to estimate the probability that the file is transferred without error. Compare this estimate to the answer obtained when you model the number of errors as a binomial random variable.

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