- The importance of probability and statistics in engineering problems
Objects of probability and statistics, the role of probability in statistics, examples of application in problems of the Civil Engineer.
- Probability theory, random variables and distribution characteristics
Sample space and events, axiomatic foundation, basic notions of combinatorial theory, conditional probability, probability, probability density and distribution functions, mean, moments of higher order, covariance and correlation, Chebyshev’s inequality, use of Monte Carlo simulation.
- Useful distribution models
Discrete distributions (binomial, hypergeometric, geometric, negative binomial, the Poisson distribution and the Poisson process), continuous distributions (normal, lognormal, uniform, exponential, gamma, Weibull, Gumbel, Pearson type ΙΙΙ, log Pearson type III).).
- Descriptive statistics
Arithmetic measures, graphical methods of exploratory data analysis, use of the Minitab package.
- Sampling distributions and estimation
Normal population theory, central limit theorem, the t, chi-square and F distributions, problems of measurements theory, confidence intervals for means, variances and proportions with one and two samples, use of the Minitab package.
- Tests of hypotheses
Errors, characteristic curve and power of a test of hypotheses, tests for means, variances and proportions with one and two samples, tests of significance, relationship between tests and confidence intervals, use of the Minitab package.
- Simple linear regression and correlation
Model assumptions, the least squares method, coefficient of determination, tests, estimation and prediction in the simple linear model, correlation analysis of two variables, use of the Minitab package.