Subject Code & Name: MA25C12 – Probability and Random Processes
Regulation: R-2025
Semester: IV (Fourth Semester)
Branch: B.E. Biomedical Engineering (BME) / B.E. Medical Electronics (MedElec)
Credits / L-T-P: 4 Credits | L-T-P: 3-1-0
Course Objectives
- Introduce concepts about random variables and random processes to compute probabilities and simulate stochastic model and analyse system responses.
Full Unit-wise Syllabus
Unit I – Probability and Random Variables
Probability axioms, Conditional probability, Total probability, Baye‘s theorem - Discrete and continuous random variables, Moments, Moment generating functions.
Activities: R programming to calculate conditional probabilities, the generation of random variables. Solving Competitive Examination questions
Unit II – Standard Distributions
Discrete distributions: Binomial, Poisson, Geometric distributions; Continuous distributions: Uniform, Exponential, Normal distributions - Functions of Random variables
Activities: Identification of industrial applications that follow the Binomial distribution, Poisson distribution, Gaussian distribution and describe their behavior and solving Competitive Examination questions.
Unit III – Two-Dimensional Random Variables
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).
Activities: Fitting a linear regression model to for real world engineering problems and solving Competitive Examination questions
Unit IV – Stochastic Processes
Classification, Stationary processes, Wide sense and strict sense stationary processes; Poisson process, Markov chain, Limiting distribution, Markov process.
Activities: Apply concepts of Markov chain and Poisson process to model real-life systems like queues and random events over time using open-source software and solving Competitive Examination questions
Unit V – Correlation and Spectral Densities
Auto correlation, Cross correlation, Properties; Power spectral density, Cross spectral density, Properties.
Activities: Create a noisy sine wave, find its Autocorrelation, and plot to see how the signal relates to itself and solving Competitive Examination questions
Unit VI – Linear Time Invariant System
Linear time invariant system, System transfer function, Linear systems with random inputs; Auto correlation and cross correlation functions of input and output.
Activities: Use open-source software to construct the system and solving Competitive Examination questions
Course Outcomes (COs)
- CO1: Understand the basic concepts of probability, random variables, standard probability distributions and random processes.
- CO2: Apply joint distributions, correlation, regression, and transformation of random variables for real-world data.
- CO3: Model and simulate random phenomena using stochastic processes and analyze their long-term behavior.
- CO4: Analyse spectral properties of random signals, autocorrelation, cross-correlation and spectral densities.
- CO5: Examine linear time invariant systems with random inputs using their transfer function
Assessment Pattern (Quick Note)
- Weightage: Continuous Assessment 40% | End Semester Examinations 60%
- Internal methodology: Assignments (20%), Solution to application-oriented problems using software (20%), Solving competitive examinations questions (20%), Internal Examinations (40%)
Source: Official Anna University – B.E. Biomedical Engineering R-2025 Syllabus
Last Updated: October 2026
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