1

Events and their probability (PDF)

2

Random variables: discrete distributions (PDF)

3

Random variables: continuous distributions (PDF)

4

Random vectors (PDF)

5

Functions of random variables and vectors (PDF)

6

Second-moment characterization of random variables and vectors; second-moment (SM) and first-order second-moment (FOSM) propagation of uncertainty (PDF)

7

Conditional second-moment analysis (PDF)

8

Selected distribution models (PDF)

9

Point and interval estimation of distribution parameters (PDF)

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

Homework 1 (PDF)

Homework 2 (PDF)

Homework 3 (PDF)

Homework 4 (PDF)

Homework 5 (PDF)

Homework 6 (PDF)

Homework 7 (PDF)

Homework 8 (PDF)

Homework 9 (PDF)

Homework 10 (PDF)

Mini-quiz 1 (PDF)

Mini-quiz 2 (PDF)

Mini-quiz 3 (PDF)

Mini-quiz 4 (PDF)

Mini-quiz 5 (PDF)

Final exam (PDF)