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On a problem in my textbook it asks to give an exact distribution of the a random variable and then in the next part it says to give a simple approximation for the same distribution. I know that the answers are binomial and poisson, respectively. My question is this: Is the poisson supposed to be regarded as an approximation to the binomial? With the poisson parameter $\mu = np$ (or $\lambda$ depending on which you use) where $n$ is the number of trials and $p$ is the probability of success in those trials.

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Yes, the Poisson distribution with $\lambda = np$ can be used to approximate the binomial distribution when $n$ is large and $p$ is small so that $np$ is a number of reasonable size.

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