MA25C12 Probability and Random Processes – Semester IV – BME / MedElec – R-2025

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