MA4114 Probability and Statistical Methods Syllabus:
MA4114 Probability and Statistical Methods Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
To provide students with basic concepts of probability theory.
To provide the most appropriate estimator of the parameter in statistical inference.
To decide whether to accept or reject a specific value of a parameters.
To avoid or at least to minimize, the problems of estimating the effects of the independent variable by experimental designs.
To learn methods for analyzing time series data to extract meaningful statistical characteristic of data.
UNIT I PROBABILITY AND RANDOM VARIABLES
Probability – Axioms of probability – Conditional probability – Baye’s theorem – Random variables – Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions – Function of a random variable.
UNIT II ESTIMATION THEORY
Principle of least squares – Regression – Multiple and partial correlations – Estimation of parameters – Maximum likelihood estimates – Method of moments.
UNIT III TESTING OF HYPOTHESIS
Sampling distributions – Small and large samples and problems – Tests based on Normal, t – distribution, Chi – square, Goodness of fit and F – distributions.
UNIT IV DESIGN OF EXPERIMENTS
Analysis of variance – Completely randomized design – Randomized block design – Latin square design – 22 Factorial designs.
UNIT V TIME SERIES
Characteristics and representation – Moving averages – Exponential smoothing – Auto regressive processes.
TOTAL : 60 PERIODS
COURSE OUTCOMES:
After completing this course, students should demonstrate competency in the following topics:
Basic probability axioms and rules and the moments of discrete and continuous random variables.
Least squares, correlation, regression, consistency, efficiency and unbiasedness of estimators, method of maximum likelihood estimation and Central Limit Theorem.
Use statistical tests in testing hypotheses on data.
List the guidelines for designing experiments and recognize the key historical figures in Design of Experiments.
Differentiate between various time series models and application of these models appropriately to engineering problems.
REFERENCES:
1. Anderson, O.D, “Time Series Analysis: Theory and Practice”, North – Holland, Amsterdam, 1982.
2. Devore, J. L., “Probability and Statistics for Engineering and Sciences”, 9th Edition, Cengage Learning, 2016.
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. Montgomery D.C and Johnson, L.A, “Forecasting and Time Series”, 6th Edition, McGraw Hill, 1990.