COLLEGE OF SCIENCE. School of Mathematical Sciences. NEW COURSE (COS-STAT-251 Probability and Statistics for Engineers I): *Approval

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1 ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences NEW COURSE (COS-STAT-251 Probability and Statistics for Engineers I): 1.0 Course Designations and Approvals Required course approvals: Approval request date: Academic Unit Curriculum Committee 10/01/10 10/01/10 College Curriculum Committee Approval granted date: Optional designations: Is designation desired? General Education: Yes No Writing Intensive: Yes No Honors: Yes No *Approval request date: **Approval granted date: 2.0 Course information: Course title: Probability and Statistics for Engineers I Credit hours: 3 Prerequisite(s): COS-MATH-182 Co-requisite(s): None Course proposed by: Daniel R. Lawrence Effective date: August, 2013 Contact hours Maximum students/section Classroom 3 50 Lab 0 Studio 0 Other (specify) 0 2.a Course Conversion Designation*** (Please check which applies to this course). *For more information on Course Conversion Designations please see page four. Semester Equivalent (SE) Please indicate which quarter course it is equivalent to: Probability and Statistics for Engineers I Semester Replacement (SR) Please indicate the quarter course(s) this course is replacing: New July 27, 2010

2 2.b Semester(s) offered (check) Fall (campus) Spring (campus) Summer Other All courses must be offered at least once every 2 years. If course will be offered on a bi-annual basis, please indicate here: 2.c Student Requirements Students required to take this course: (by program and year, as appropriate) Industrial and Systems Engineering Students (3 rd year) and Biomedical Engineering Students (3 rd year). Students who might elect to take the course: Anyone interested in the field possessing the appropriate background, primarily students in engineering, math, or computing. In the sections that follow, please use sub-numbering as appropriate (eg. 3.1, 3.2, etc.) 3.0 Goals of the course (including rationale for the course, when appropriate): 3.1 To acquaint students with basic techniques of probability and descriptive statistics. 3.2 To introduce to the students the basic discrete and continuous probability models. 3.3 To provide the students with the necessary background for inferential statistics, mathematical modeling and related subjects. 3.4 To provide the student with the knowledge of the application of probability and descriptive statistics to real-world problems. 4.0 Course description Course: COS-STAT-251 Probability and Statistics for Engineers I Statistics in engineering; enumerative and analytic studies; descriptive statistics and statistical control; sample spaces and events; axioms of probability; counting techniques; conditional probability and independence; distributions of discrete and continuous random variables; joint distributions; central limit theorem. Prerequisite(s): COS-MATH-173 or COS-MATH-182 or COS-MATH-182a Class 3, Credit 3 (Fall, Spring) 5.0 Possible resources (texts, references, computer packages, etc.) 5.1 Probability and Statistics for Engineering and the Sciences, Devore, J. L. (2008), Duxbury. 5.2 Minitab software 2

3 6.0 Topics (outline): 6.1 Graphical Summaries (in the One-Sample Case) 6.2 Measures of Location 6.3 Measures of Variability 6.4 Sample Spaces and Events 6.5 Axioms & Properties of Probability 6.6 Counting Techniques 6.7 Conditional Probability 6.8 Independence 6.9 Random Variables 6.10 Discrete Random Variables (RVs) General Case 6.11 Expected Values 6.12 Binomial, Hypergeometric, Negative-Binomial, Poisson 6.13 Continuous RVs General Case 6.14 Expected Values 6.15 Normal, Gamma, Other Continuous RVs 6.16 Probability Plots 6.17 Jointly Distributed RVs 6.18 Statistics and their Distributions 6.19 Distribution of the Sample Mean (Central Limit Theorem) and Linear Combinations 7.0 Intended course learning outcomes and associated assessment methods of those outcomes (please include as many Course Learning Outcomes as appropriate, one outcome and assessment method per row). Course Objectives Level 1: Knowledge: 1.1.Write formulas for sample means, medians, variance, and standard deviation. Do the same for population quantities, for both the discrete and continuous cases 1.2.Write formulas for combinatorial and permutation functions. 1.3.Write definitions of conditional probability, of independence of events, of disjoint events. 1.4.Write definition of expected value for discrete and continuous random variables. Level 2: Comprehension: 2.1.Explain the Central Limit Theorem and its use in probability. 2.2.Explain how the distribution of sample means and linear combinations of random variables are related to the original distribution. Level 3: Application: 3.1.For a given set of data, calculate sample means, medians, variance, standard deviation, range. Assessment Method Homework Exams Projects 3

4 3.2.For a given dotplot, histogram, or boxplot of independent data from one sample, determine whether the data appear to come from a symmetric or skewed distribution, and whether there are outliers in the data. 3.3.For a given problem, write down the sample space. 3.4.For a given sample space, set of events, and basic probabilities, calculate the probabilities of intersections and unions of such events. 3.5.For given discrete distribution (Hypergeometric, Binomial, Negative-Binomial, Poisson), calculate probabilities for that distribution by hand. (Also do so in software, using Minitab.) 3.6.For a given continuous distribution (Normal, Exponential, or other) and either a table (Normal) or formula (Exponential or other), calculate probabilities for that distribution. (Also do so in software, such as Minitab.) 3.7.For a given joint distribution (discrete, or continuous with easily integrable density function) calculate marginal and conditional probabilities for that distribution. 3.8.For a given set of data, use software to construct a Normal probability plot and follow rules to decide whether the data is from a Normal distribution. Level 4: Analysis: 4.1.For a given problem, classify the problem into discrete or continuous, further classify the problem into the most reasonable distribution, and further determine whether that distribution is correct from the problem statement or needs to be examined in the data analysis itself. 4

5 8.0 Program outcomes and/or goals supported by this course Relationship to Program Outcomes (1 = slightly, 2=moderately, 3=significantly) Level of Program Outcomes and/or Goals for Undergraduate Engineers Support (specific engineering programs will have more specific ABET outcomes) Demonstrates an solid understanding of statistical thinking and applied statistics methodology in solving real-world problems Designs studies that are efficient and valid Analyzes data using appropriate statistical methods Communicates the results of statistical analysis with effective reports and presentations. 9.0 General Education Learning Outcome Supported by the Course, if appropriate Communication Express themselves effectively in common college-level written forms using standard American English Revise and improve written and visual content Express themselves effectively in presentations, either in spoken standard American English or sign language (American Sign Language or English-based Signing) Comprehend information accessed through reading and discussion Intellectual Inquiry Review, assess, and draw conclusions about hypotheses and theories Analyze arguments, in relation to their premises, assumptions, contexts, and conclusions Construct logical and reasonable arguments that include anticipation of counterarguments Use relevant evidence gathered through accepted scholarly methods and properly acknowledge sources of information Ethical, Social and Global Awareness Analyze similarities and differences in human experiences and consequent perspectives Examine connections among the world s populations Identify contemporary ethical questions and relevant stakeholder positions Scientific, Mathematical and Technological Literacy Explain basic principles and concepts of one of the natural sciences Apply methods of scientific inquiry and problem solving to contemporary issues Comprehend and evaluate mathematical and statistical information Assessment Method Exams Exams 5

6 Perform college-level mathematical operations on quantitative data Describe the potential and the limitations of technology Use appropriate technology to achieve desired outcomes Creativity, Innovation and Artistic Literacy Demonstrate creative/innovative approaches to course-based assignments or projects Interpret and evaluate artistic expression considering the cultural context in which it was created Exams 10.0 Other relevant information (such as special classroom, studio, or lab needs, special scheduling, media requirements, etc.) None *Optional course designation; approval request date: This is the date that the college curriculum committee forwards this course to the appropriate optional course designation curriculum committee for review. The chair of the college curriculum committee is responsible to fill in this date. **Optional course designation; approval granted date: This is the date the optional course designation curriculum committee approves a course for the requested optional course designation. The chair of the appropriate optional course designation curriculum committee is responsible to fill in this date. ***Course Conversion Designations Please use the following definitions to complete table 2.a on page one. Semester Equivalent (SE) Closely corresponds to an existing quarter course (e.g., a 4 quarter credit hour (qch) course which becomes a 3 semester credit hour (sch) course.) The semester course may develop material in greater depth or length. Semester Replacement (SR) A semester course (or courses) taking the place of a previous quarter course(s) by rearranging or combining material from a previous quarter course(s) (e.g. a two semester sequence that replaces a three quarter sequence). New (N) No corresponding quarter course(s). 6