Students are expected to understand the basic concepts of probability theory and to apply this theory in the engineering field.
Prerequisite(s)
MCB1002 - Calculus II
Corequisite(s)
None
Special Requisite(s)
Read, understand, formulate, explain, and apply mathematical statements, and state and apply important results in key mathematical areas (Calculus I and Calculus II).
Textbook: Douglas C. Montgomery, George C. Runger, "Applied Statistics and Probability for Engineers", 6e ISV, 2014.
Lecture Notes: CATS
Other Sources
1. Sheldon M. Ross, "Introduction to Probability Models", Academic Press, 10th Edition, 2009.
2. Irwin Miller and Marylees Miller, “John E. Freund's Mathematical Statistics with Applications”, Pearson; 8th Edition, 2018.
Course Schedules
Week
Contents
Learning Methods
1. Week
The Role of Probability and Statistics in Engineering
Lectures and recitation
2. Week
Sample Spaces and Events, Interpretations and Axioms of Probability, Addition Rules
Lectures and recitation
3. Week
Conditional Probability, Multiplication and Total Probability Rules, Independence
Lectures and recitation
4. Week
Bayes' Theorem
Lectures and recitation
5. Week
Random Variables
Lectures and recitation
6. Week
Discrete Random Variables, Probability Distributions and Probability Mass Functions, Cumulative Distribution Functions
Lectures and recitation
7. Week
Mean and Variance of a Discrete Random Variable, Discrete Uniform Distribution, Binomial Distribution
Lectures and recitation
8. Week
Midterm
9. Week
Geometric and Negative Binomial Distributions
, Poisson Distribution
Lectures and recitation
10. Week
Continuous Random Variables, Probability Distributions and Probability Density Functions, Cumulative Distribution Functions, Mean and Variance of a Continuous Random Variable, Continuous Uniform Distribution
Lectures and recitation
11. Week
Normal Distribution, Normal Approximation to the Binomial and Poisson Distributions, Exponential Distribution
Lectures and recitation
12. Week
Erlang and Gamma Distributions, Weibull Distribution
Lectures and recitation
13. Week
Two or more Random Variables, Covariance and Correlation, Common joint distributions
Lectures and recitation
14. Week
Linear Functions of Random Variables, General Functions of Random Variables
Lectures and recitation
15. Week
General Review
Final
16. Week
Final Week
Final
17. Week
Final Week
Final
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
30
Quizzes
6
20
Homework / Term Projects / Presentations
5
0
Final Exam
1
40
Program Outcomes
PO-1
Ability to apply theoretical and practical knowledge gained by Mathematics, Science and their engineering fields and ability to use their knowledge in solving complex engineering problems.
PO-2
Ability of determining, defining, formulating and solving complex engineering problems; for that purpose develop the ability of selecting and implementing suitable models and methods of analysis.
PO-3
Ability of designing a complex system, process, device or product under real world constraints and conditions serving certain needs; for this purpose ability of applying modern design techniques
PO-4
Ability of selecting and using the modern techniques and devices which are necessary for analyzing and solving complex problems in engineering implementations; ability of efficient usage of information technologies.
PO-5
Ability of designing experiments, conducting tests, collecting data and analyzing and interpreting the solutions to investigate of complex engineering problems or discipline-specific research topics.
PO-6
Ability of working efficiently in intra-disciplinary and multi-disciplinary teams; individual working ability and habits.
PO-7
Ability of verbal and written communication skills; and at least one foreign language skills, ability to write effective reports and understand written reports, ability to prepare design and production reports, ability to make impressive presentation, ability to give and receive clear and understandable instructions
PO-8
Awareness of importance of lifelong learning; ability to access data, to follow up the recent innovation in science and technology for continuous self-improvement.
PO-9
Conformity to ethical principles; knowledge about occupational and ethical responsibility, and standards used in engineering applications.
PO-10
Knowledge about work life implementations such as project management, risk management and change management; awareness about entrepreneurship and innovativeness; knowledge about sustainable development.
PO-11
Knowledge about effects of engineering applications on health, environment and security in global and social dimensions, and on the problems of the modern age in engineering; awareness about legal outcomes of engineering solutions.
Learning Outcomes
LO-1
Gains the ability to comprehend the basic probability concept, apply counting techniques and calculate the probability of an event.
LO-2
Gains the ability to distinguish basic probability terminology such as random experiment, result, sample space, event, random variable, etc.
LO-3
Gains the ability to construct a probability function, cumulative density function, probability mass function, or probability density function for a random variable and use them in problem-solving.
LO-4
Gains the ability to use the concepts of mathematical expectation and variance.
LO-5
Gains the ability to distinguish special probability functions and understand where/when to use them.
