MA4108 Applied Probability and Statistical Analysis Syllabus:

MA4108 Applied Probability and Statistical Analysis Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES :

 To provide students with basic concepts of probability theory.
 To gain knowledge about two dimensional random variable and its regression, correlations.
 To decide whether to accept or reject a specific value of the parameters.
 To provide the most appropriate interval estimator of the parameters in statistical inferences.
 To avoid or at least minimize, the problems of estimating the effects of the independent variables by experimental designs.

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 TWO DIMENSIONAL RANDOM VARIABLES

Joint distributions – Marginal and conditional distributions – Functions of two dimensional random variables – Regression curve – Correlation.

UNIT III TESTING OF HYPOTHESIS

Sampling distributions – Type I and Type II errors – 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 IV ESTIMATION THEORY

Interval estimation for population mean – Standard deviation – Difference in means, proportion ratio of standard deviations and variances.

UNIT V DESIGN OF EXPERIMENTS

Completely randomized design – Randomized block design – Latin square design – 2² Factorial design.

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 and various standard distributions and their properties.
 Distributions of two dimensional variables, correlation and regression.
 Use statistical tests in testing hypotheses on data.
 Interval estimation for population parameters such as mean and standard deviation.
 List the guidelines for designing experiments and recognize the key historical figures in Design of Experiments.

REFERENCES:

1. Devore, J. L., “Probability and Statistics for Engineering and Sciences”, 8th Edition, Cengage Learning, 2014.
2. Gupta S.C. and Kapoor V.K.,” Fundamentals of Mathematical Statistics”, 12th Edition, Sultan and Sons, New Delhi, 2020.
3. Johnson, R.A., Miller, I and Freund J., “Miller and Freund’s Probability and Statistics for Engineers”, 9th Edition, Pearson Education, Asia, 2016.
4. Rice, J. A., “Mathematical Statistics and Data Analysis”, 3rd Edition, Cengage Learning, 2015.
5. Ross, S. M., “Introduction to Probability and Statistics for Engineers and Scientists”, 5th Edition, Elsevier, 2014.