Textbook readings are given as page numbers from this text:

Ang, Alfredo H-S., and Wilson H. Tang. *Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering*. 2nd ed. New York, NY: John Wiley & Sons, 2006. ISBN: 9780471720645.

The following table provides information about the lecture (L) and recitation (R) sessions, and also shows when each of the lecture notes and application examples are presented.

SES # | LECTURE TOPICS | TEXTBOOK READINGS | NOTES | EXAMPLES | KEY DATES |
---|---|---|---|---|---|

Events, their probability, and two important theorems | |||||

L1 | Introduction. Events and their properties | 27-43 | |||

L2 | Probability of events. Conditional probability, total probability theorem | 44-63 | 1 | ||

L3 | Independence, Bayes' theorem | 63-65 | 1 | 2, 3, and 4 | Homework 1 out |

R1 | Total probability and Bayes' theorems | ||||

Random variables | |||||

L4 | Discrete random variables. Bernoulli and geometric distributions | 81-88 and 105-111 | 5 | ||

L5 | Binomial and Poisson distributions | 112-118 | 2 | 6 |
Homework 1 due Homework 2 out |

R2 | Discrete random variables | ||||

L6 | Continuous random variables. Uniform and exponential distributions | 118-122 | |||

L7 | Hazard function, distributions of mixed type and distribution mixtures | 3 | 7 and 8 |
Homework 2 due Homework 3 out | |

R3 | Continuous random variables, and hazard function | Quiz 1 | |||

Random vectors | |||||

L8 | Discrete random vectors | ||||

L9 | Continuous random vectors | 131-136 | 4 | 9 |
Homework 3 due Homework 4 out |

R4 | Random vectors | ||||

Uncertainty propagation | |||||

L10 | Functions of random variables; linear functions | 151-156 | |||

L11 | Functions of random variables and vectors; monotonic and min/max functions | 157-160 and 172-174 | 10, 11, and 12 |
Homework 4 due Homework 5 out | |

R5 | Functions of random variables | Quiz 2 | |||

L12 | Functions of random vectors: sums of variables, gamma distribution | 122-125 | 5 | ||

Second moment analysis | |||||

L13 | Expectation, second moment characterization of random variables, probabilistic moments | 88-93 | Homework 5 due | ||

R6 | Functions of random variables and vectors | ||||

L14 | Second moment (SM) and first order second moment (FOSM) propagation of uncertainty for variables | 180-186 | Homework 6 out | ||

L15 | Second moment characterization of random vectors; covariance and correlation coefficient | 138-140 | |||

R7 | Probabilistic moments, SM and FOSM propagation of uncertainty for variables | Quiz 3 | |||

L16 | SM and FOSM propagation of uncertainty for random vectors | 186-189 | Homework 6 due | ||

L17 | SM and FOSM propagation of uncertainty for random vectors | 6 | 13 and 14 | Homework 7 out | |

R8 | Variance, covariance, correlation, SM and FOSM propagation of uncertainty for random vectors | ||||

Conditional second moment analysis | |||||

L18 | Conditional SM analysis for variables | ||||

L19 | Conditional SM analysis for vectors | 7 | 15 and 16 |
Homework 7 due Homework 8 out | |

R9 | Conditional SM analysis for variables | Quiz 4 | |||

Important distribution models | |||||

L20 | Normal and lognormal distributions | 96-105 |
Homework 8 due Homework 9 out | ||

R10 | Conditional SM analysis. Important distribution models | ||||

L21 | Beta, extreme, and multivariate normal distributions | 127-131, 137, and 175-179 | 8 | 17 and 18 | |

Statistics | |||||

L22 | Estimation of distribution parameters: general principles | Homework 9 due | |||

R11 | Estimation of distribution parameters | Quiz 5 | |||

L23 | Method of moments | 246-251 | Homework 10 out | ||

L24 | Maximum likelihood and Bayesian estimation | 251-254 and 346-357 | 9 | 19 | Homework 10 due |

L25 | Simple and multiple linear regression | 306-309, 313-318, and 321-325 | |||

R12 | Maximum likelihood and Bayesian estimation | ||||

L26 | Pre-final review |