Application Examples

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

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