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