## Elements of Probability and Statistics: An Introduction to Probability with de Finetti’s Approach and to Bayesian StatisticsThis book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics. |

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### Contents

3 | |

2 Discrete Distributions | 27 |

3 OneDimensional Absolutely Continuous Distributions | 43 |

4 Multidimensional Absolutely Continuous Distributions | 57 |

5 Convergence of Distributions | 73 |

6 Discrete Time Markov Chains | 81 |

7 Continuous Time Markov Chains | 89 |

8 Statistics | 103 |

13 Markov Chains | 181 |

14 Statistics | 197 |

Appendix AElements of Combinatorics | 213 |

Appendix BRelations Between Discrete and AbsolutelyContinuous Distributions | 216 |

Appendix CSome Discrete Distributions | 217 |

Appendix DSome OneDimensional AbsolutelyContinuous Distributions | 218 |

Appendix EThe Normal Distribution | 219 |

Appendix FStirlings Formula | 220 |

Part II Exercises | 114 |

9 Combinatorics | 117 |

10 Discrete Distributions | 127 |

11 OneDimensional Absolutely Continuous Distributions | 142 |

12 Absolutely Continuous and Multivariate Distributions | 151 |

Appendix GElements of Analysis | 231 |

Appendix HBidimensional Integrals | 235 |

242 | |

243 | |