MA25C11 Probability, Statistical and Random Processes – Semester III – ECE / VLSI / ElecComp – R-2025

Subject Code & Name: MA25C11 – Probability, Statistical and Random Processes

Regulation: R-2025

Semester: III (Third Semester)

Branch: B.E. Electronics and Communication Engineering (ECE) / B.E. Electronics Engineering (VLSI) / B.E. Electronics and Computer Engineering (ElecComp)

Credits / L-T-P: 4 Credits | L-T-P: 3-1-0

Course Objectives

• To provide a rigorous mathematical foundation in statistical analysis and probability theory required for industrial quality control, semiconductor manufacturing, signal processing, and modern communication systems.
• The course emphasizes "small sampling theory" and stochastic processes essential for electronics R&D.

Full Unit-wise Syllabus

Unit I – Descriptive and Bivariate Statistics

Univariate Measures: Mean, Median, Mode, Variance, and Standard Deviation, Relative Variation: Coefficient of Variation (CV) for comparing component stability., Bivariate Statistics: Covariance and the Correlation Coefficient (r), Linear Regression: Method of Least Squares for sensor calibration and trend analysis

Unit II – Probability Foundations and Distributions

Probability Theory: Axioms, Conditional Probability, and Bayes’ Theorem (Signal Detection). Random Variables: Discrete (Binomial, Poisson for shot noise) and Continuous (Uniform, Exponential). The Normal Distribution: Properties of Gaussian distributions, Central Limit Theorem, and Z-scores. ● Multivariate Gaussian: Joint PDFs, independence, and correlation in vector random variables.

Unit III – Statistical Inference and Small Sampling

Sampling Distributions: Population vs. Sample; Degrees of Freedom. Small Sample Tests: Student’s t-distribution (One-sample and Two-sample tests). Variance Analysis: Chi-square distribution and F-distribution for comparing production batches. Estimation: Confidence Intervals for mean and variance of device parameters.

Unit IV – Hypothesis Testing and Error Metrics

Testing Framework: Null (H0) and Alternative (H1) Hypotheses. Decision Errors: Type I error (Alpha), Type II error (Beta), and Power of a test. p-values: Interpretation of p-values in industrial datasheets and medical electronics. Parametric & Non-Parametric: ANOVA basics and Chi-square Goodness-of-Fit tests.

Unit V – Stochastic Processes and Signal Noise

Random Processes: Concept of Stationarity (WSS) and Ergodicity. Correlation Dynamics: Auto-correlation and Cross-correlation functions. Frequency Domain: Power Spectral Density (PSD) and Wiener-Khinchin Theorem. LTI Systems: Response of linear circuits to random noise; Introduction to the Kalman Filter.

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 analysis.
• CO3: Model and simulate random phenomena using stochastic processes and analyze their long term behavior.
• CO4: Analyze spectral properties of random signals including autocorrelation, cross correlation, and spectral density functions.
• CO5: Examine linear time invariant systems with random inputs using transfer function analysis and stochastic system modeling.

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. Electronics and Communication Engineering R-2025 Curriculum
Last Updated: September 2026