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Engineering Probability and Statistics - SE-205 -Chap 1 By S. O. Duffuaa Course Objectives Introduce the students to basic probability and statistics and demonstrate its wide application in the area of Systems Engineering. Main Course Outcomes Students should be able to perform: • • • • Summarize and present data using graphs, diagrams and point summaries. Define, compute probability using basic probability laws and concepts. Define and describe a random variable. Describe known probability distributions in terms pmf/pdf, distribution function, mean, variance, and suggest few applications for each distribution. Main Course Outcomes • • • • Calculate probabilities from probability mass and density functions.. Perform point and interval estimation. Use a statistical package such as Minitab/Statistica to solve problems in data analysis, probability distribution, and estimation. Work in teams and communicate effectively through class presentations and group meetings. Text Book and References “Applied Statistics and Probability for Engineers “ by D. C. Montgomery and Runger, 2007. “Probability and Statistics for Engineers and Scientists” 5th by Walpole and Mayers. Statistics by Murry Speigel Course Policy Home-works and attendance Quizzes Exam1 Exam II Final Exam 15% 15% 20% 20% 30% SE- 205 Place in SE Curriculum Central Course Prerequisite for 7 SE courses • SE 303, SE 320, SE 323, SE 325, SE 447, SE 480, SE 463 and may be others. See SE Curriculum Tree Engineering Problem Solving Develop clear and concise problem description Identify the important factors in the problem. Propose a model for the problem Conduct appropriate experimentation Refine the model Engineering Problem Solving Validate the solution Conclusion and recommendations Statistics • Science of data collection, summarization, presentation and analysis for decision making. • • • • How to collect data ? How to summarize it ? How to present it ? How do you analyze it and make conclusions and correct decisions ? Role of Statistics Many aspects of Engineering deals with data – Product and process design Identify sources of variability Essential for decision making Data Collection Observational study • Observe the system • Historical data The objective is to build a system model usually called empirical models Data Collection Design of experiment • Plays key role in engineering design Statistics Divided into : • Descriptive Statistics • Inferential Statistics Forms of Data Description Point summary Tabular format Graphical format Diagrams Point Summary Central tendency measures • Mean xi/n • Median --- Middle value • Mode --- Most frequent value Point Summary Variability measures • Range = Max xi - Min xi • Variance = V = (xi – x )2/ n-1 • Standard deviation = S S = Square root (V) • Coefficient of variation = S/ x Dot Diagram A diagram that has on the x-axis the points plotted : Given the following grades of a class: 50, 23, 40, 90, 95, 10, 80, 50, 75, 55, 60, 40. . . . . 0 50 100 Dot Diagram A diagram that has on the x-axis the points plotted : Given the following grades of a class: 50, 23, 40, 90, 95, 10, 80, 50, 75, 55, 60, 40. . . . . 0 50 100 Time Frequency Plot 15 14 13 12 11 y 10 9 8 7 6 5 0 10 20 30 Observation number 40 50 Time Frequency Plot 15 14 13 12 11 y 10 9 8 7 6 5 0 10 20 30 Observation number 40 50 Control Charts 105 Concentration Upper control limit = 100.5 95 x = 91.50 85 Lower control limit = 82.54 75 0 10 20 Observation number 30