L 4 C 4
Teachers Continuous Evaluation: 40 marks. Term-End Semester Examination: 60 marks.
Course outcomes
- Analyze multivariate random variables and probability models for engineering applications.
- Characterize random processes using statistical measures such as correlation functions, stationarity, and spectral density.
- Apply Markov chains, Poisson processes, and queueing models for performance analysis of stochastic engineering systems.
- Develop stochastic and reliability models for analyzing uncertain engineering systems and real-world applications.
Unit I
Review of random variables and probability distributions, Joint probability distributions, Marginal and conditional probability distributions, Independence of random variables, Functions of two or more random variables, Transformation of random variables, Distribution of functions of random variables, Mathematical expectation of functions of random variables, Joint moments, Covariance and correlation coefficients, Moment generating functions, Characteristic functions, Applications of random variable models in engineering systems.
Unit II
Introduction to random processes, Classification of random processes, Discrete-time and continuous-time random processes, Ensemble averages, Mean function, Autocorrelation function, Cross-correlation function, Covariance function, Stationary random processes, Wide-sense stationary processes, Ergodic processes, Gaussian random processes, White noise processes, Power spectral density, Relationship between autocorrelation and power spectral density, Linear systems with random inputs.
Unit III
Markov chains, Discrete-time Markov chains, Transition probability matrix, Chapman–Kolmogorov equations, Classification of states, Periodicity and recurrence, Steady-state probabilities, Continuous-time Markov chains (basic concepts), Poisson processes, Birth-death processes, Introduction to queueing theory, Queueing models and Kendall notation, M/M/1 and M/M/c queueing systems, Little’s theorem, Applications of queueing models in computer and communication networks.
Unit IV
Reliability concepts, Reliability function, Failure rate and hazard function, Mean time to failure, Series and parallel reliability models, Standby systems, Availability and maintainability, Renewal process (basic concepts), Monte Carlo simulation methods for stochastic systems, Applications of stochastic processes in communication systems, signal processing, computer networks, manufacturing systems, and machine learning.
Textbooks
- A. Leon-Garcia, Probability, Statistics, and Random Processes for Electrical Engineering, 3rd ed. Boston, MA, USA: Pearson, 2008.
References
- A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 5th ed. New York, NY, USA: McGraw-Hill Education, 2002.
- S. M. Ross, Introduction to Probability Models, 12th ed. Amsterdam, The Netherlands: Academic Press, 2019.
- R. D. Yates and D. J. Goodman, Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 3rd ed. Hoboken, NJ, USA: John Wiley & Sons, 2014. th
- H. Stark and J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers, 4 ed. Upper Saddle River, NJ, USA: Prentice Hall, 2011.
- D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability, 2nd ed. Nashua, NH, USA: Athena Scientific, 2008.