Luca Lista's Statistical Methods for Data Analysis in Particle Physics PDF

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Extra resources for Statistical Methods for Data Analysis in Particle Physics

Sample text

This is already partially evident in Fig. 1, where the distribution of the sum of two dice rolls is peaked around 7 (D 2 3:5 D 2 hxi) even for N D 2. This convergence of the probability distribution of xN to the single value hxi, for N ! 1, is called law of large numbers, and can be illustrated in a simulated experiment consisting of repeatedly rolling a dice, whose result ranges from 1 to 6 as usual, and plotting the average xN obtained after the first N extractions, as a function of N. This is shown in Fig.

Particle detectors are examples of such devices. The distribution of the number of positive signals n upon 16 1 Probability Theory Fig. 8 The Yang Hui triangle published in 1303 by Zhu Shijie (1260–1320) the occurrence of N processes of interest is given by a binomial distribution with probability p D ". 05 0 0 2 4 6 8 10 12 14 n Fig. 8 efficiency " of the device. The problem of parameter estimates will be discussed more in general in Chaps. 3 and 5 for what concerns the Bayesian and frequentist approaches, respectively.

1)”. In practice, anyway, we know that experiments are reproducible on a finite range of time (on this planet, for instance, until the sun and the solar system will continue to exist), so, for the practical purposes of physics application, we can consider the law of large numbers and the frequentist definition of probability, beyond their exact mathematical meaning, as pragmatic definitions that describe to a very good approximation level the concrete situations of the vast majority of the cases we are interested in experimental physics.

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