The application examples in this section provide worked examples on several topics and supplement the lecture notes.

EXAMPLES | TITLES | TOPICS |
---|---|---|

1 | Reliability of systems with various element configurations ( PDF) | Probability of combinations of events; binomial and Poisson distributions |

2 | Evaluation of natural and man-made risks ( PDF) | Total probability theorem |

3 | Extra-terrestrial life and the design of experiments ( PDF) | Bayes’ theorem |

4 | Earthquake prediction from imperfect premonitory signs ( PDF) | Bayes’ theorem (cont.) |

5 | Is the series of rainy/non-rainy days a Bernoulli trial sequence? ( PDF) | Bernoulli trial sequence and dependence in binary time series |

6 | Are the sequences of bus and earthquake arrivals Poisson? ( PDF) | Exponential and Poisson distributions |

7 | Distribution mixtures ( PDF) | Distribution mixtures |

8 | Old better than new, new better than old… ( PDF) | Hazard function |

9 | Relation between storm duration and precipitation intensity ( PDF) | Joint, marginal and conditional distributions |

10 | Reliability of a building under extreme wind loads: choosing the design wind speed ( PDF) | Independent random variables |

11 | Distribution of the maximum of independent identically-distributed variables ( PDF) | Functions of several random variables |

12 | Distribution of waves and wave loads in a random sea ( PDF) | Functions of random variables and reliability analysis |

13 | Design load factors for structural columns ( PDF) | Propagation of uncertainty through linear formulas: second-moment analysis |

14 | Probabilistic analysis of foundation settlement ( PDF) | FOSM analysis for functions of many variables |

15 | Uncertainty updating using noisy observations ( PDF) | Conditional second-moment analysis |

16 | Prediction of daily temperatures using several past observations ( PDF) | Conditional second moment analysis with vectors |

17 | Sums of iid random variables ( PDF) | Sums of iid random variables |

18 | Designing the checkout system of a supermarket ( PDF) | Stochastic system; Monte Carlo simulation |

19 | Comparison of estimators for the upper limit of the uniform distribution ( PDF) | Parameter estimation |