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planetmath.org | ||
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www.johndcook.com
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| | | | | Analogs of Euler's formula exp(ix) = cos(x) + i sin(x) in other number systems, namely dual numbers and double numbers. | |
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thatsmaths.com
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| | | | | We are all familiar with Pascal's Triangle, also known as the Arithmetic Triangle (AT). Each entry in the AT is the sum of the two closest entries in the row above it. The $latex {k}&fg=000000$-th entry in row $latex {n}&fg=000000$ is the binomial coefficient $latex {\binom{n}{k}}&fg=000000$ (read $latex {n}&fg=000000$-choose-$latex {k}&fg=000000$), the number of ways of... | |
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www.randomservices.org
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| | | | | [AI summary] The text presents a comprehensive overview of the beta-Bernoulli process and its related statistical properties. Key concepts include: 1) The Bayesian estimator of the probability parameter $ p $ based on Bernoulli trials, which is $ rac{a + Y_n}{a + b + n} $, where $ a $ and $ b $ are parameters of the beta distribution. 2) The stochastic process $ s{Z} = rac{a + Y_n}{a + b + n} $, which is a martingale and central to the theory of the beta-Bernoulli process. 3) The distribution of the trial number of the $ k $th success, $ V_k $, which follows a beta-negative binomial distribution. 4) The mean and variance of $ V_k $, derived using conditional expectations. 5) The connection between the beta distribution and the negative binomial distributi... | |
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sriku.org
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| | | [AI summary] The article explains how to generate random numbers that follow a specific probability distribution using a uniform random number generator, focusing on methods involving inverse transform sampling and handling both continuous and discrete cases. | ||
