## MA3391 Syllabus - Probability And Statistics - 2021 Regulation Anna University

MA3391

PROBABILITY AND STATISTICS

LTPC

3104

COURSE OBJECTIVES:
• This course aims at providing the required skill to apply the statistical tools in engineering problems.
• To introduce the basic concepts of probability and random variables.
• To introduce the basic concepts of two dimensional random variables.
• To acquaint the knowledge of testing of hypothesis for small and large samples which plays an important role in real life problems.
• To introduce the basic concepts of classifications of design of experiments which plays very important roles in the field of agriculture and statistical quality control.

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UNIT I

PROBABILITY AND RANDOM VARIABLES

9+3

Axioms of probability – Conditional probability – Baye’s theorem - Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions – Functions of a random variable.

UNIT II

TWO- DIMENSIONAL RANDOM VARIABLES

9+3

Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables).

UNIT III

ESTIMATION THEORY

9+3

Unbiased estimators - Efficiency - Consistency - Sufficiency - Robustness - Method of moments - Method of maximum Likelihood - Interval estimation of Means - Differences between means, variations and ratio of two variances

UNIT IV

NON- PARAMETRIC TESTS

9+3

Introduction - The Sign test - The Signed - Rank test - Rank - sum tests - The U test - The H test - Tests based on Runs - Test of randomness - The Kolmogorov Tests.

UNIT V

STATISTICAL QUALITY CONTROL

9+3

Control charts for measurements ( and R charts ) – Control charts for attributes ( p, c and np charts) – Tolerance limits - Acceptance sampling.

TOTAL: 60 PERIODS

COURSE OUTCOMES: Upon completion of the course, students will be able to:
• Understand the fundamental knowledge of the concepts of probability and have knowledge of standard distributions which can describe real life phenomenon.
• Understand the basic concepts of one and two dimensional random variables and apply in engineering applications.
• Apply the concept of testing of hypothesis for small and large samples in real life problems.
• Apply the basic concepts of classifications of design of experiments in the field of agriculture and statistical quality control.
• Have the notion of sampling distributions and statistical techniques used in engineering and management problems.

TEXT BOOKS:
1. Johnson. R.A., Miller. I.R and Freund . J.E, " Miller and Freund’s Probability and Statistics for Engineers", Pearson Education, Asia, 9th Edition, 2016.
2. Milton. J. S. and Arnold. J.C., "Introduction to Probability and Statistics", Tata Mc Graw Hill, 4 th Edition, 2007.
3. John E. Freund , " Mathematical Statistics " , Prentice Hall, 5 th Edition, 1992.

REFERENCES:
1. Gupta. S.C. and Kapoor. V. K., “Fundamentals of Mathematical Statistics”, Sultan Chand & Sons, New Delhi, 12th Edition, 2020.
2. Devore. J.L., "Probability and Statistics for Engineering and the Sciences”, Cengage Learning, New Delhi, 8th Edition, 2014.
3. Ross . S.M., "Introduction to Probability and Statistics for Engineers and Scientists", 5 thEdition, Elsevier, 2014.
4. Spiegel. M.R., Schiller. J. and Srinivasan . R.A., "Schaum’s Outline of Theory and Problems of Probability and Statistics", Tata McGraw Hill Edition, 4th Edition, 2012.
5. Walpole. R.E., Myers. R.H., Myers. S.L. and Ye. K., "Probability and Statistics for Engineers and Scientists", Pearson Education, Asia, 9th Edition, 2010.