## Probability for PhysicistsThis book is designed as a practical and intuitive introduction to probability, statistics and random quantities for physicists. The book aims at getting to the main points by a clear, hands-on exposition supported by well-illustrated and worked-out examples. A strong focus on applications in physics and other natural sciences is maintained throughout. In addition to basic concepts of random variables, distributions, expected values and statistics, the book discusses the notions of entropy, Markov processes, and fundamentals of random number generation and Monte-Carlo methods. |

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### Contents

3 | |

2 Probability Distributions | 31 |

3 Special Continuous Probability Distributions | 65 |

4 Expected Values | 93 |

5 Special Discrete Probability Distributions | 122 |

6 Stable Distributions and Random Walks | 143 |

Part II Determination of Distribution Parameters | 175 |

7 Statistical Inference from Samples | 177 |

Part III Special Applications of Probability
| 282 |

11 Entropy and Information | 283 |

12 Markov Processes | 307 |

13 The MonteCarlo Method | 325 |

14 Stochastic Population Modeling | 347 |

Appendix A Probability as Measure
| 360 |

Appendix B Generating and Characteristic Functions
| 365 |

Appendix C Random Number Generators
| 381 |

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### Common terms and phrases

algorithm approximation arbitrary average binomial distribution calculate Cauchy Cauchy distribution central limit theorem chain characteristic function coefficient compute conditional probability continuous random variable convolution correlation corresponding covariance matrix curve decay defined definition domain degrees of freedom denote dependence detector determine deviation discrete distributed according distribution function equal equation error estimate event expected value exponentially distributed formula fX(x hence initial integral likelihood likelihood function limit theorem linear log2 measure method minimal moment-generating function mutually independent observations obtained outcomes parameters particles points Poisson distribution polynomial population probability density probability distribution Probability for Physicists problem quantile random numbers random walks regression sample mean sample space Sect sequence shown in Fig Širca ſº standardized normal distribution statistical uncertainties uniform distribution var|X vector velocity zero