Course

Unit 1

Sample Space and Events, Interpretations and Axioms of Probability, Addition rules, Conditional Probability, Multiplication and Total Probability rules, Independence, Bayes theorem.

Unit 2

Random variables, Probability Distributions and Probability mass functions, Cumulative Distribution functions, mathematical expectation, variance, moments and moment generating function.

Unit 3

Standard discrete distributions – Binomial, Poisson, Uniform, Geometric distributions, Negative binomial and Hypergeometric Distributions -Standard continuous distributions – Uniform, Exponential, Gamma, Beta and Normal distributions. Chebyshevs theorem.

Unit 4

Two dimensional random variables -Joint, marginal and conditional probability distributions for discrete and continuous cases, independence, expectation of two dimensional random variables – conditional mean, conditional variance, covariance and correlation.

Unit 5

Functions of one and two random variables. Sampling and sampling Distributions- t, F and Chi square distributions. Central limit theorem.

Text Books / References

Text Books:

1. Douglas C. Montgomery and George C. Runger, Applied Statistics and Probability for Engineers, 6^thEdition, John Wiley and Sons Inc., (2017)
2. K. Rohatgi and A. K. Md. E. Saleh, An Introduction to Probability and Statistics, 3^rdEdition, Wiley, (2025)
3. Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye, Probability and Statistics for Engineers and Scientists, 9^thEdition, Pearson Education Asia, (2024).

References

1. Ross S.M., Introduction to Probability and Statistics for Engineers and Scientists, 6^thedition, Elsevier Academic Press, (2021)
2. Ravichandran, J. Probability and Statistics for engineers, New Edition, Wiley India, 2023.

This course introduces the fundamental concepts of probability and statistics essential for practical applications. It covers probability theory, random variables, standard probability distributions, and Chebyshevs inequality for real-world modelling. The course also examines joint random variables, correlation, and covariance using practical data. Further, it emphasizes sampling distributions and the Central Limit Theorem to understand the behaviour of sample statistics for inference and decision-making under uncertainty.

Course Outcomes: After successful completion of the course, students will be able to

1. Understanding the foundations of probability theory and exploring the relationship between events.
2. Studying the behavior of random variables and their distributions and properties.
3. Understand the real time problems and the statistical distributions that will often be
4. Used for modelling andapplications Chebyshev’ sinequality.
5. Investigating the joint behaviour of multiple random variables and their relationship using real time data.
6. Understanding the behaviour of sample statistics, Samplingdistributions and Central Limit Theorem

CO-PO Mapping: