MA4071 Applied Probability and Statistics for Design Engineers Syllabus:
MA4071 Applied Probability and Statistics for Design Engineers Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
To compute moments of standard distributions.
To gain the knowledge about correlation and regression.
To provide the most appropriate estimator of the parameter in statistical inference.
To decide whether to accept or reject specific value of a parameters.
To understand many real-world problems fall naturally within the frame work of multivariate normal theory.
UNIT – I ONE DIMENSIONAL RANDOM VARIABLES
Random variables – Probability functions – Moments – Moment generating functions and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions – Function of a random variable.
UNIT – II TWO DIMENSIONAL RANDOM VARIABLES
Joint distributions – Marginal and conditional distributions – Functions of two dimensional random variables – Correlation – Linear Regression.
UNIT- III ESTIMATION THEORY
Unbiased estimators – Method of moments – Maximum likelihood estimation – Principle of least squares – Regression lines.
UNIT – IV TESTING OF HYPOTHESIS
Sampling distributions – Type I and Type II errors – Small and large samples – Tests based on Normal, t, Chi square and F distributions for testing of mean, variance and proportions – Tests for independence of attributes and goodness of fit.
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
COURSE OUTCOMES:
After completing this course, students should demonstrate competency in the following topics:
Moments of discrete and continuous random variables.
To deal problems involving two dimensional random variables.
Unbiasedness of estimators, method of maximum likelihood estimation and Central Limit Theorem.
Use statistical tests in testing hypotheses on data.
Perform exploratory analysis of multivariate data, such as multivariate normal density, calculating descriptive statistics, testing for multivariate normality.
REFERENCES :
1. Devore, J. L., “Probability and Statistics for Engineering and the Sciences”, 8th Edition, Cengage Learning, 2014.
2. Dallas E. Johnson, “Applied Multivariate Methods for Data Analysis”, Thomson and Duxbury press, 1998.
3. Gupta S.C. and Kapoor V.K.,” Fundamentals of Mathematical Statistics”, 12th Edition, Sultan and Sons, New Delhi, 2020.
4. Johnson, R.A., Miller, I and Freund J., “Miller and Freund’s Probability and Statistics for Engineers “, 9th Edition, Pearson Education, Asia, 2016.
5. Richard A. Johnson and Dean W. Wichern, “Applied Multivariate Statistical Analysis”, 6th Edition, Pearson Education, Asia, 2012.