A simple alternative to the binomial distribution that places more probability weight on the tails is considered. Its derivation only requires the weighted arithmetic mean of two discrete probability mass functions, one being the binomial itself and the other being the bi-uniform introduced here. Some properties are derived, and an application to a classical data set is discussed. The presentation can be seen as an exemplary treatise on how to construct a statistical model, derive statistical properties, fit models to actual data by employing estimation methods, and verify appropriateness by using elements from statistical hypothesis testing.
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