BSc in Mechanical Engineering

Course Details

Course Information Package

Course Unit TitlePROBABILITY AND STATISTICS
Course Unit CodeAMAT300
Course Unit DetailsBSc Mechanical Engineering (Required Courses) - BSc Civil Engineering (Required Courses) - BSc Quantity Surveying (Required Courses) -
Number of ECTS credits allocated5
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
  1. Use descriptive statistics to present data by constructing Bar Charts, Pie Charts, Histograms and Box Plots.
  2. Explain and apply measures of central tendency such as mean, median and mode, measures of Dispersion such as Range, IQR, Variance and standard deviation and the coefficients of Variation and Skewness to different types of data.
  3. Describe the notion of sample space for an experiment, describe events as subsets of the sample space and construct events by using set theoretic operations and with the use of Venn diagrams.
  4. Construct the probability function on the space of events with its properties, define conditional probability and calculate probabilities of events in simple problems.
  5. Describe the concepts of discrete and continuous random variables as functions from the sample space to the set of real numbers and explain and use the probability distribution function and cumulative distribution function to calculate simple probabilities.
  6. Calculate the expected number, variance and standard deviation of a random variable and use discrete and continuous distributions in examples to calculate probabilities in real life problems.
  7. Calculate point estimators and construct confidence intervals for means and proportions of one and two populations.
  8. Test hypothesis for means, proportions and difference of means, apply hypothesis testing to real life problems and construct linear models for a given set of data using linear regression.
Mode of DeliveryFace-to-face
PrerequisitesAMAT122Co-requisitesNONE
Recommended optional program componentsNONE
Course Contents

Descriptive Statistics: Introduction to Statistics, Data Collection, Describing and Summarizing Data, Measures of Central Tendency, Dispersion and Skewness, Tables, Charts, Exploratory Data Analysis.

Probability: Sample Spaces and Events. Introduction to set theory and relations in set theory. Definitions of Probability and properties. Conditional probability.

Discrete Random Variables: Probability Distribution Function and cumulative distribution function, Mathematical Expectation, Mean and Variance. Probability Distributions: Binomial, Poisson.

Continuous Random Variables: Probability density Function and cumulative distribution function, Mathematical Expectation, Mean and Variance. Probability Distributions: Uniform, Normal Distribution. Approximations for Discrete Distributions.

Sampling distributions: Properties of sample distributions: Unbiasedness and minimum variance. The central limit theorem.

Estimation: Confidence Internal Estimation for Mean, Proportion, Difference of Means, Difference of Proportions.  Sample size determination.

Hypothesis Testing: Hypothesis Testing for Mean, Proportion, Difference of Means, Difference of Proportions.

Introduction to regression: Simple Linear Regression and Correlation

Recommended and/or required reading:
Textbooks
  • Morris H. DeGroot, Mark Schervish, Probability and Statistics, 2001
References
  • Paterson, Hennessy, Computer Organization and Design: the Hardware/Software Interface, Morgan Kaufman, 2008
  • M.L. Beverson, D.M. Levine, and D. Rindskopf, Applied Statistics, A first course, Prentice-Hall Int. Editions
  • J. T. McClave, T. Sincich, W. Mendenhall, Statistics, 11th Ed., Prentice Hall, 2007
Planned learning activities and teaching methods

The taught part of course is delivered to the students by means of lectures, conducted with the help of computer presentations. Lecture notes and presentations are available through the web for students to use in combination with the textbooks.

Several examples and exercises are solved in class to practice the theory and methodology taught. Students are then asked to work on their own during class hours on examples and practice problems. Extra assignments are given to students to tackle at home.

Assessment methods and criteria
Tests40%
Final Exam60%
Language of instructionEnglish
Work placement(s)NO

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