Introduction to probability emphasizing applications in engineering. Topics include the use of discrete and continuous random variables, Goodness of Fit Tests, fitting of distributions, and elementary stochastic processes. This course is cross-listed with STAT 2620.

Prerequisites & Corequisites: Prerequisites: IME 2610 and MATH 2720 with concurrency.

Credits: 3 hours

Lecture Hours - Laboratory Hours: (3 to 0)

• IME 2610 - Engineering Statistics
• MATH 2720 (or concurrent) - Differential and Integral Multivariate Calculus

At the end of the semester, students should be able to:

1. To apply the basic rules and theorems of probability theory to engineering problems. {a, b, e, k}
2. To appropriately choose, define and/or derive probability distributions for use in engineering models. {a, b, e, k}
3. To develop functions of random variables that can be used in decision making.
   {a, b, e, k}
4. To construct and utilize basic quality models for the management, control, and improvement of systems and processes. {a, b, c, e, k}

The student should be able to:

Objective 1

1. Understand and apply basic probability concepts, such as the definitions of an element, set, sample space, event, probability, and conditional probability. [1, 2, 3]
2. Use counting rules and logic to assign probabilities to events. [1, 2, 3]
3. Apply probability axioms and theorems, such as Bayes' Theorem, to determine probabilities that help to solve engineering problems. [1, 2, 3]
4. Determine whether two, or more events, are mutually exclusive or statistically independent. [1, 2, 3]

Objective 2

1. Define a discrete random variable, and its associated p.m.f. and c.d.f. [1, 2, 3]
2. Define a continuous random variable, and its associated p.d..f. and c.d.f. [1, 2, 3]
3. Appropriately use named distributions, such as the Binomial and the Normal, to model and solve engineering problems. [1, 2, 3]
4. Determine the expectation and variance of a random variable from its distribution. [1, 2, 3]
5. Fit data to an appropriate distribution through statistical tests, such as Regression, Chi-Square Goodness of Fit tests and others. [1, 2, 3]

Objective 3

1. Derive a probability distribution for the function of a random variable, along with its associated expectation and variance. [1, 2, 3]
2. Properly utilize joint distributions to solve engineering problems. [1, 2, 3]
3. Define and interpret the covariance and the correlation coefficient associated with the joint distribution of two random variables. [1, 2, 3]
4. Employ the conditional distributions and expectations of jointly distributed random variables to make engineering decisions. [1, 2, 3]

Objective 4

4.1 Understand the fundamentals of quality and the methods used to control systems and processes.
4.2 Select and apply fundamental quality improvement tools including flowcharting, cause & effect diagrams, and Pareto analysis.
4.3 Comprehend the concept of statistical process control and be able to set up and interpret both variable and attribute control charts.
4.4 Understand and apply lot-by-lot acceptance sampling.
4.5 Conduct and interpret the results of a process capability analysis.
4.6 Assess the adequacy of a measurement system.
4.7 Understand the basic concepts underlying Six Sigma Methodologies
4.8 Take the Quality Engineer Certification (CQE) Exam from the American Society for Quality

Probability and Statistics for Engineers and Scientists (with CD-ROM), 3rd edition
Anthony J. Hayter
ISBN: 0495107573
Duxbury Press (Thompson Brooks/Cole), 2007 (required)

Software:

MINITAB Statistical Software, Release 14

Crystal Ball 7, Decisioneering Inc., Denver, Colorado (required)

Steven E. Butt, Ph.D.