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.