Probability Theory – Statistics

Learning Results

Upon successful completion of this course, students will have obtained comprehensive knowledge on the main concepts of Probability Theory and Statistics. Students will learn to quantize events, reason on how probable an event is, determine how to calculate conditional probability and how and if two events are independent. They will also understand, via the Bayes theorem, how a prior understanding of an event can be modified when new data emerges and how strong do the data need to be in this case. Students will learn to identify the different distributions that data follow and especially the Normal Distribution. They will also become familiar with two-dimensional variables and how we can measure their covariance and/or correlation. This course lays out the foundation needed for a wide range of applications of probability theory that students will come across during their studies.

Skills acquired

Research, analysis and synthesis of the data and information, using the appropriate equipment, Working into an interdisciplinary environment, Producing new research ideas, Promotion of free, creative and inductive thinking.

Revision of Set and Counting Theory, probability, conditional probabilities, event independence, Bayes theorem and Law of Total Probability, Random Variables, probability density functions, cumulative distribution functions, Properties of a Random Variable, discrete distributions (Binomial, Geometric, Negative Binomial, Poisson, etc), continuous distributions (Exponential, Uniform, Normal), Two dimensional random variables (discrete and continuous), jointly distributed random variables, properties of two dimensional random variables, covariance and correlation of two random variables.

1. Douglas C. Montgomery, George C. Runger, “Applied Statistics and Probability for Engineers”, 6th edition, Wiley, 2013, ISBN: 9781118539712
2. Sheldon Ross, “A first course in Probability”, 8th edition, Pearson Prentice Hall, 2009, ISBN: 978-0136033134
3. Hossein Pishro-Nik, “Introduction to Probability, Statistics, and Random Processes”, 1st edition, Kappa Research, 2014, ISBN: 978-0990637202
4. William Mendenhall, Robert J. Beaver, Barbara M. Beaver, “Introduction to Probability and Statistics”, 15th edition, Cengage Learning, 2019, ISBN: 978-1337554428
5. Richard A. Johnson, “Miller & Freund’s Probability and Statistics for Engineers”, 9th Edition, Pearson, ISBN: 978-0321986245