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

Course Info

Learning Resource Types

assignment Problem Sets
grading Exams
notes Lecture Notes