Introduction : Role of Probability in Civil Engineering Problems; Examples.
Random Events : Definition of basic random events; Application of set theory in definition of composite event operations;
Probability of events and definition of probability axioms; Solution of real life examples from civil engineering.
Random Variables : Definition of random variables – discrete and continuous;Probability definitions – PMF, PDF, CDF;Moments and expectations.
Functions of Random Variables : Definition of probability distributions of functions of single random variables – exact methods and approximate methods;Moments and expectations of functions – direct and indirect methods.
Multiple Random Variables : Definition of joint, marginal, and conditional probability distributions;Definitions of moments and expectations, including the definition of correlation coefficient;Functions of multiple random variables.
Common Probability Models : Discrete random variables – binomial distribution, Poisson’s distribution;
Continuous random variables – exponential distribution, gamma distribution;
Central limit theorem; Normal and lognormal distributions; Extremal distributions.
Statistics and sampling : Goodness of fit tests; regression and correlation analyses; estimation of distribution parameters from statistics;
Hypothesis testing and significance; Bayesian updating of distributions.
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