Probability Fact

Daily tweets on probability from @JohnDCook.

[Probability Fact @ProbFact]

Putting probability to work

https://t.co/yyp1rEw9hL

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Explaining probability to a jury https://t.co/BsfyN7LjKv

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The problem w/ trying to achieve reliability w/ multiple software implementations: they're not independent.

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A Short Introduction to Optimal Transport and Wasserstein Distance https://t.co/hDVRu2zL2J

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Uniformity increases entropy https://t.co/MysOEBZL6R

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A random number generator may have excellent statistical properties and yet be unsuited for cryptography.

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Let τ be Kendall's tau and let ρ be Spearman's rho. Then -1 ≤ 3τ - 2ρ ≤ 1.

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'All probabilities are conditional on something, and to be useful they must condition on the right thing.' -- Frank Harrell

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Cosine power approximation to normal https://t.co/XwICbxK8fq

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The moment generating function of a random variable X is the two-sided Laplace transform of its density function f_X, with the sign of the argument flipped.

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The Mellin transform of the product of two independent random variables is the product of their Mellin transforms.

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Perfect and imperfect shuffles https://t.co/urTCPVh6lb

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'There are only five probabilities the average human can handle: 99 percent, one percent, 100 percent, zero, and 50-50. That’s it.” — Richard Thaler

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Coefficient of variation = standard deviation / mean

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If A and B are independent causal factors leading to L, then L is called a collider. After conditioning on L, A and B are /not/ independent.

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Counting selections with replacement https://t.co/ZG5nGOVR1u

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For a multivariate normal, the probability of being within two standard deviations of the mean goes to zero as the dimension increases.

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Tweedie distributions https://t.co/4SLeqr7EX4

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Logs, Tails, Long Tails https://t.co/P6zLoM77pL

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Pairwise independence does not imply independence https://t.co/VO5WWFPWBJ

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The Laplace (double exponential) distribution is commonly used for noise generation in differential privacy applications.