At the end of the course, the student can …
- Recall and explain basic terminology and concepts of probability and statistics;
- Reason about choosing and applying elementary models and techniques of probability and statistics (see ‘content description’ for the list of models and techniques);
- Apply elementary models and techniques of probability and statistics, work out their solution to obtain correct (numerical) results, and explain their solution;
- Properly interpret the results (described above);
- Apply the knowledge of Statistics in the project of this module
This is a part of module 11, ME 11 Production Systems Engineering of the Bachelor Mechanical Engineering.. See here for the complete description of the module.|
In contemporary research and in practice we often have to work with data. In many practical scenarios, the data can be seen as a result of a random experiment (e.g. measurements, or lifetime of equipment). When the number of measurements is sufficiently large, we can find patterns in such data. This is useful for making predictions and planning, e.g. in supply chains or production systems.
Probability theory is useful for studying such patterns, based on specific assumptions about the random experiment, which we call a probabilistic model. For example, we could assume that a random filter has an average lifetime of 162,000,000 km, and plan maintenance and replacement of filters, based on this assumption.
Statistics is the science that, based on real data, investigates whether the assumptions of such a probabilistic model (and the conclusions that are derived from it) fit with reality. For instance, measurements may show that the average lifetime (in km) of 200 air filters in ship engines is 161,800,000 km.
Does the somewhat smaller measured average disprove the initial assumption or is it a result of random fluctuations?
In this course, the students will learn how to answer such questions using basic models and methods of probability and statistics.
Models and techniques discussed in this course are: random experiment, sample space, probability, conditional probability, independence, random variables, discrete probability distributions (Binomial, Geometric, Hypergeometric and Poisson distributions), continuous probability distributions (Uniform, Normal and Exponential distributions), joint distributions, conditional distributions, expectation, variance, covariance, correlation coefficient, weak law of large numbers, estimators, unbiased estimators, mean square error, confidence intervals, prediction intervals, basic concepts of hypothesis testing, one-sample and two-sample problems.
Non-ME students can take this course if they meet the entry requirements.
Assumed previous knowledge
|Self-diagnostic tests and submission of the Case Study Assignment will be mandatory to access the Final Assignment.|
|Bachelor Mechanical Engineering||Required materials|
Recommended materials-Instructional modes
|Douglas C. Montgomery, George C. Runger, "Applied Statistics and Probability for Engineers", 7-th edition, Wiley, ISBN 9781119585596|
|Videos: Vimeo links provided on Canvas. The full list is also available on YouTube.|
|Matlab: Statistics package, usually available in the standard version.|
|Self study without assistance|