COURSE: CENG 114 Probability and Statistical Methods for Engineers

DESCRIPTION: Probability theory, conditional probability, Bayestheorem,random variables, densities, expected values, central limit theorem. Engineering reliability, elements of estimation, random sampling, sampling distributions, hypothesis testing, confidence intervals. Curve fitting and data analysis.

PREREQUISITES: None

TEXTBOOK, REQUIRED MATERIALS:
  • Digital Inclusive: Connect Access For Statistics For Engineers & Scientists (includes Ebook), 4 Edition, 9781260113433.

CLASS/LABORATORY SCHEDULE: Four hours of lecture, eight hours outside preparation. 12 hours/week total (estimated)

COURSE TOPICS:
  • Introduction to probability theory, conditional probability, and Bayes theorem;
  • Random variables, continuous vs. discrete, expected values, central limit theorem;
  • Elements of estimation, random sampling, sampling distributions;
  • Hypothesis testing and confidence intervals;
  • Curve fitting and data analysis;
  • Analysis of Variance (ANOVA)

COURSE OBJECTIVES:

1. To teach students the mathematical basis to quantify uncertainties in problems in engineering.
2. To enable students to formulate and solve engineering problems which are not deterministic but instead have to be addressed using probabilistic and statistical tools (5e, 8h)
3. To demonstrate the application of probability and statistics to the analysis of real-life engineering data.

METHODS OF EVALUATION:
  1. 1. Homework
  2. 2. Midterm exams
  3. 3. Final exam

PERFORMANCE CRITERIA:
Objective1
1.1 Students will demonstrate understanding of the basic principles of probability theory. For example, using conditional probabilities to decompose a single event into multiple upstream events; or using Bayes theorem to invert conditional probabilities

Objective2
2.1 Students will learn to manipulate random variables as mathematical descriptors of events. For example, derive the probability density functions and probability mass functions of events described in words; or translate mathematically elementary manipulations of set theory learned in Objective1.

Objective3
3.1 Students will learn the methods of estimation of parameters, apply them to data drawn from real-life engineering examples, and exploit them for interval estimation. For example, they will be able to estimate mean and standard deviation; or derive confidence intervals with a known variance with a given confidence level.

Objective4
4.1 Students will learn the mathematical basis of curve fitting for data drawn from real-life examples. For example, they will able to do a least-squares linear fit to a set of data points.

CONTRIBUTION OF COURSE TO PROFESSIONAL COMPONENT:
Provides necessary background and enables students to analyze engineering problems with nondeterministic ingredients.