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Lecture notes on Monte Carlo simulations

Lecture notes onMonte Carlo simulationsPeter OlssonApril 4, 2022iiContents1 Buffon s needle .. Models in Physics .. Different kinds of Monte Carlo simulations .. 32 Random variables and Distributions .. Estimation .. Error estimates of averages variance of the mean .. Generating random variables .. Sampling a distribution with Markovchains .. 173 The Lennard-Jones Summary of different ensembles .. Gibbs entropy formula .. Monte Carlo versus Molecular Dynamics.

The binomial distribution The binomial distribution appears whenever the outcome may be classified into two mutually exclusive classes, x= 0, 1. The distribution is then p(x) = (1− α, x= 0, α, x= 1, or p(x) = α x(1− α)(1− ),

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