## MA4155 Applied Probability and Statistics for Manufacturing Engineering Syllabus:

MA4155 Applied Probability and Statistics for Manufacturing Engineering Syllabus – Anna University PG Syllabus Regulation 2021

### COURSE OBJECTIVES:

1. To understand the basics of random variables with emphasis on the standard discrete and continuous distributions.

2. To understand the basic probability concepts with respect to two dimensional random variables along with the relationship between the random variables.

3. To apply the small and large sample tests through test of hypothesis.

4. To understand the basic concepts of sampling distributions and statistical properties of point estimators.

5. To understand the concept of analysis of variance and use it to investigate factorial dependence.

### 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 – 2^{2} Factorial design.

### COURSE OUTCOMES:

At the end of the course, students will be able to

1. Analyze the performance in terms of probabilities and distributions achieved by the determined solutions.

2. Be familiar with some of the commonly encountered two dimensional random variables and be equipped for a possible extension to multivariate analysis.

3. Apply the basic principles underlying statistical inference(hypothesis testing).

4. Demonstrate knowledge of applicable large sample theory of estimators and tests.

5. Obtain a better understanding of the importance of the methods in modern industrial processes.

### 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.