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# Normal approximation to Poisson distribution

Course Topic(s): Probability | Continuous Distributions, normal | Discrete Distribution, Poisson | Convergence Theorems, central limit theorem

Normal Approximation to Poisson is justified by the Central Limit Theorem. If $$Y$$ denotes the number of events occurring in an interval with mean $$\lambda$$ and variance $$\lambda$$, and $$X_1, X_2,\ldots, X_\ldots$$ are independent Poisson random variables with mean 1, then the sum of $$X$$'s is a Poisson random variable with mean $$\lambda$$. This site provides analytical description of this fact and includes an example.

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Subject classification(s): Univariate Distributions | Probability | Statistics and Probability

Creator(s): PSU STAT 415 Instructors

Contributor(s): PSU STAT 415 Instructors

This resource was cataloged by Ivo Dinov

Publisher:
The Pennsylvania State University

This review was published on September 19, 2012