Upon successful completion of the course, the students will have a good understanding of the fundamental principles of probability and probability distributions of random variables, as well as their application to problems of engineering. Further, they will be able to do the basic statistical analysis of data of one and two quantities (random variables) in engineering problems. Specifically, they will be able to estimate main statistical characteristics of the variable of interest, such as the mean and variance, reporting the estimation accuracy, as well as the (linear) correlation and regression of two variables of interest.
Course Content (Syllabus)
Probability space, conditional probability, total probability, Bayes’ theorem. Random variables. Distribution functions of discrete and continuous random variables. Theoretical distributions (binomial, geometric, negative geometric, hypergeometric, Poisson, uniform, normal, exponential). Characteristics and parameters of distributions (mean value, variance, other moments, mode, Tchebycheff inequality). Functions of random variables.
Descriptive statistics of data (summary statistics and graphs). Estimation of distribution parameters from observations of a random variable, properties of estimators, the method of moments and the method of maximum likelihood, estimation of confidence interval for the mean, variance and difference of two means. Regression and correlation analysis, simple linear regression.