Credits: 3


Prerequisite: MATH206 and ENME392.
Restriction: Permission of ENGR-Mechanical Engineering department.
Review of probabilistic distributions, introduction to pseudo-random number generation, and algorithms to produce probability distributions using Monte Carlo simulation via Matlab and other approaches to best design probabilistic engineering problems.

Semesters Offered

Spring 2019, Spring 2020, Spring 2021

Learning Objectives

  • Develop an ability to solve basic probability problems using known distributions (e.g., normal, Poisson, Bernoulli, etc.)
  • Understand how pseudo-random numbers are generated as well as maximizing the period until these numbers are repeated
  • Develop an ability to simulate both discrete and continuous probability distributions using several well-known approaches such as:
    • Inverse transformation method
    • Central limit theorem (for normal distribution)
    • Acceptance-Rejection method
  • Explore queueing theory models and discrete-event simulation
  • Understand the tradeoffs between increasing the number of simulation iterations and the variance of the simulated output  Develop an ability to apply several variance-reduction methods such as:
    • Antithetic variables
    • Control variates
  • Understand and be able to apply Bayes theorem in engineering problems
  • Be able to apply simulation methods to analyze two case studies in engineering
  • Enhance a working knowledge of Matlab geared to solving Monte Carlo simulation problems


Topics Covered

  • Week 1:  Introduction, motivation for simulation, review of Matlab
  • Week 2:  Probability review, Bernoulli & binonmial distribtions
  • Week 3:  Uniform and triangular distributions, pseudo-random number generation
  • Week 4:  Exponential and geometric distributions , normal distribution, lognormal distribution
  • Week 5:  Generating discrete and continuous distributions for random variables
  • Week 6:  Generating discrete and continuous distributions for random variables
  • Week 7:  Normal distribution and Central Limit Theorem with relevance to simulation, in-class exam #1
  • Week 8:  Specialized approaches for generating normal random variables
  • Week 9:  Background on wind power and the Weibull distribution for wind speeds, Betz’ law for wind power, discussion of case study 1 on renewable energy
  • Week 10:  Poisson distribution and Bayes theorem, goodness-of-fit measures
  • Week 11:  Case study 1 final presentations, report of results, case study 2 overview, variance reduction techniques
  • Week 12:  Variance reduction techniques, discrete event simulation and queueing disciplines
  • Week 13:  Open class to discuss case study 2, in-class exam #2
  • Week 14:  Case Study 2 final presentations, report of results, review for final exam
  • Week 15: Final exam (in-class exam)


Learning Outcomes

  • an ability to apply knowledge of mathematics, science, and engineering
  • an ability to design and conduct experiments, as well as to analyze and interpret data
  • an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
  • an ability to function on multi-disciplinary teams
  • an ability to identify, formulate, and solve engineering problems
  • an ability to communicate effectively
  • the broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
  • a recognition of the need for, and an ability to engage in life-long learning
  • a knowledge of contemporary issues
  • an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice

Additional Course Information


Gabriel, Steven A.


Simulation, Sheldon M. Ross, Fifth Edition, Academic Press, San Diego, 2013

Class/Laboratory Schedule 

  • Two 75 minute lectures each week
Last Updated By 
Steven A. Gabriel, June 2017