Titlebook: Digressions in Elementary Probability; The Unexpected in Me Edward Beltrami Book 2024 The Editor(s) (if applicable) and The Author(s), unde

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Restricted Choice,The simplest and perhaps most persuasive argument for the selection bias was provided by Miller and Sanjurjo [6] employing Bayes Theorem and I can do no better than to follow their reasoning and even some of their wording.

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,Another Conundrum: What Does the Crowd Size at Wimbledon’s Tennis Match Tell Us About Baseball BattI want to discuss a curious finding that appears to defy intuition. I begin by reviewing a classical estimation procedure in which we have a random variable having a normal density function with unknown average or mean θ and a unit variance. What needs to be estimated is the unknown mean θ.

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Medical Misreadings,In the previous section we saw that a random sample of per-capita cancer rates by county can exhibit considerable variation depending on sample size.

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What Are the Odds of That?,The spooky quality of coincidences rarely fails to fascinate and confound people who experience them. What I hope to show is that many, perhaps most, coincidences are less amazing than they first appear to be.

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,Turing’s Evidence,Most accounts of Alan Turing’s time at Bletchley Park focus on his achievements in breaking the Enigma code but until 2012 little was known about his use of Bayesian methods to solve problems in cryptology. I give here a brief summary of how Turing approached one such problem following the historical summaries in Zabell [39] and Simpson [38].

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The Paradox of Random Arrivals,This section and the one that follows are a bit more technical and makes use of continuous random variables unlike the rest of this book.

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Arezou Yaghoubian,Junko Ozao-Choyven below. The key insight for interpreting their results is a very simple property of the Poisson distribution, namely that the mean and variance are the same, and this is the reason why this is of interest to us.

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