The probability distribution of a Poisson random variable provides a good model for data that represent the number of occurrences of a specified event in a given unit of time or space.

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The Poisson distribution is commonly used to model count data, such as the number of earthquakes in a region or the number of customers who enter a store. It assumes that the occurrences are random and independent, and that the average rate of occurrences is constant over time or space. Therefore, it is a suitable model for data that meet these assumptions.

The Probability Distribution of a Poisson Random Variable Provides a Good