23MAT206-PROBABILITY AND STATISTICS
About Course
Probability and Statistics is a fundamental branch of mathematics that deals with the collection, analysis, interpretation, and presentation of data. It helps in understanding uncertainty, making predictions, and drawing meaningful conclusions from numerical information. Probability focuses on measuring the likelihood of events occurring, while Statistics involves organizing and analyzing data to support decision-making in various fields such as science, engineering, business, economics, medicine, and technology. This course introduces students to concepts such as random variables, probability distributions, sampling methods, hypothesis testing, correlation, regression, and statistical inference. By studying Probability and Statistics, learners develop analytical thinking, problem-solving abilities, and data interpretation skills that are essential for research, data science, machine learning, and real-world applications.
Course Content
Syllabus
COURSE OBJECTIVES:
᧢ To develop Probability techniques in manufacturing and quality evaluation process.
᧢ To acquaint the knowledge of testing of hypothesis for small and large samples which plays an important role in real life problems.
UNIT I PROBABILITY AND RANDOM VARIABLES 9
Axioms of probability - Conditional probability - Total probability - Baye᧙s theorem- Discrete and continuous random variables ᧓ Moments.
UNIT II STANDARD DISTRIBUTIONS 9
Binomial ᧓ Poisson ᧓ Exponential ᧓ Normal distributions ᧓ Moment generating functions and their properties.
UNI*******WO DIMENSIONAL RANDOM VARIABLES 9
Joint distributions ᧓ Marginal and conditional distributions ᧓ Covariance ᧓ Correlation and linear regression ᧓ Central limit theorem(Statement only).
UNIT IV TESTING OF HYPOTHESIS 9
Sampling distributions ᧓ Statistical hypothesis ᧓ Tests for single mean, proportion, Difference of means (large and small samples) ᧓ Tests for single variance and equality of variances ᧓ Chi square test for goodness of fit-Independence of attributes.
UNIT V DESIGN OF EXPERIMENTS 9
One way and two way classifications ᧓ Completely randomized design ᧓ Randomized block design ᧓ Latin square design.
L:45 T:0 P: 0 Total: 45 Periods
TEXT BOOKS
T1 Ibe, O.C., Fundamentals of Applied Probability and Random Processes, Elsevier, 1st Indian Reprint, 2016.
T2 Papoulis, A and Unnikrishnapillai, S., Probability, Random Variables and Stochastic Processes McGraw Hill Education India, 4th Edition, New Delhi, 2010.
REFERENCES
R1 Walpole. R.E., Myers. R.H., Myers. S.L., and Ye. K., Probability and Statistics for Engineers and Scientists,9th Edition, Pearson Education, Asia, 2010.
R2 Trivedi, K.S., Probability and Statistics with Reliability, Queuing and Computer Science Applications, PHI Learning Private limited , New Delhi ,2011.
R3 Devore. J.L., "Probability and Statistics for Engineering and the Sciences", Cengage Learning, New Delhi, 8 th Edition, 2014.
R4 Ross, S.M., Introduction to Probability and Statistics for Engineers and Scientists, 3rd Edition, Elsevier, 2004.
R5 Spiegel,M.R., Schiller, J. and Srinivasan,R.A., "Schaum᧙s Outlines on Probability and Statistics, Tata McGraw Hill edition, 4th Edition, 2012.
LECTURE NOTES
PUZZLES
RESOURCE LINKS
ASSIGNMENTS
GRADES AND TOPPERS
QUESTION BANK
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