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Central limit theorem In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed. That is, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a "bell curve"). The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed.
The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of numbers that start with that digit. Frequency of first significant digit of physical constants plotted against Benford's law Benford's Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data.
By ESTHER LANDHUIS Persi Diaconis has spent much of his life turning scams inside out. In 1962, the then 17-year-old sought to stymie a Caribbean casino that was allegedly using shaved dice to boost house odds in games of chance. In the mid-1970s, the upstart statistician exposed some key problems in ESP research and debunked a handful of famed psychics. Magician-turned-mathematician uncovers bias in coin flipping
Fundamentals of Mathematics