MA5165 STATISTICAL METHODS FOR ENGINEERS SYLLABUS
REGULATIONS 2017
ANNA UNIVERSITY M.E SEMESTER 1
OBJECTIVES :
This course is designed to provide the solid foundation on topics in various statistical methods which form the basis for many other areas in the mathematical sciences including statistics, modern optimization methods and risk modeling. It is framed to address the issues and the principles of estimation theory, testing of hypothesis, correlation and regression, design of experiments and multivariate analysis.
UNIT I ESTIMATION THEORY
Estimators : Unbiasedness, Consistency, Efficiency and sufficiency – Maximum likelihood estimation – Method of moments.
UNIT II TESTING OF HYPOTHESIS
Sampling distributions - Small and large samples -Tests based on Normal, t, Chi square, and F distributions for testing of means, variance and proportions – Analysis of r x c tables – Goodness of fit.
UNIT III CORRELATION AND REGRESSION
Multiple and partial correlation – Method of least squares – Plane of regression – Properties of residuals – Coefficient of multiple correlation – Coefficient of partial correlation – Multiple correlation with total and partial correlations – Regression and partial correlations in terms of lower order co - efficient.
UNIT IV DESIGN OF EXPERIMENTS
Analysis of variance – One way and two way classifications – Completely randomized design – Randomized block design – Latin square design - 2 2 Factorial design.
UNIT V MULTIVARIATE ANALYSIS
Random vectors and matrices – Mean vectors and covariance matrices – Multivariate normal density and its properties – Principal components : Population principal components – Principal components from standardized variables.
TOTAL: 60 PERIODS
OUTCOMES :
After completing this course, students should demonstrate competency in the following topics: Consistency, efficiency and unbiasedness of estimators, method of maximum likelihood estimation and Central Limit Theorem. Use statistical tests in testing hypotheses on data. Concept of linear regression, correlation, and its applications. List the guidelines for designing experiments and recognize the key historical figures in Design of Experiments. Perform exploratory analysis of multivariate data, such as multivariate normal density, calculating descriptive statistics, testing for multivariate normality. The students should have the ability to use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.
REFERENCES :
1. Gupta.S.C., and Kapoor, V.K., “Fundamentals of Mathematical Statistics”, Sultan Chand and Sons, 11th Edition, 2002.
2. Jay L. Devore, “Probability and statistics for Engineering and the Sciences”, 8th Edition, Cengage Learning, 2014.
3. Johnson, R.A. and Wichern, D. W. “Applied Multivariate Statistical Analysis”, Pearson Education, Asia, 6th Edition, 2007.
4. Johnson, R.A., Miller, I and Freund J., "Miller and Freund’s Probability and Statistics for Engineers", Pearson Education, Asia, 8th Edition, 2015.
5. Rice, J.A. "Mathematical Statistics and Data Analysis", 3rd Edition, Cengage Learning, 2015.
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