COURSE CONTENT

1. The importance of probability and statistics in engineering problems

Objects of probability and statistics, the role of probability in statistics, examples of application in engineer’s problems.

2. 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

3. Useful distribution models

Discrete distributions (binomial, hypergeometric, geometric, negative binomial, the Poisson distribution and the Poisson process), continuous distributions (normal, uniform, exponential, gamma, Weibull).

4. Descriptive statistics

Arithmetic measures, graphical methods of exploratory data analysis.

5. 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.

6. 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 hypothesis tests and confidence intervals.

LEARNING OUTCOMES

This course is the basic introductory course in Probability and Statistics.

The main purpose of the course is to familiarize students with the basic theory and laws of probability and the widely used functions and parameters of description of probability distributions. In addition, the course aims at acquainting with useful discrete and continuous distribution models for calculating probabilities of engineer problems and to present methods of data analysis using graphical tools and descriptive statistical measures.

Finally, the course also aims to familiarize the students with the use of appropriate statistics for conducting hypothesis testing and construct confidence intervals for population parameters.

Upon successful completion of the course the student will be able to:

• select and apply appropriate discrete and continuous distribution patterns to find probabilities, percentage points and return periods.
• analyzes data using descriptive statistics tools.
• uses appropriate sampling measures to calculate confidence intervals for the mean, the variance, and proportions.
• using the hypothesis testing and confidence interval procedures for decision making.