SYLLABUS
MA25C05
Probability, Statistical and Random Processes

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.
Probability Foundations and Distributions
Probability Theory: Axioms, Conditional Probability, and Baye’s
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
Statistical inference and small sampling
Sampling distributions: Population vs. Sample: Degrees of Freedom.
Small 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.
Hypothesis testing and Error metrics
Testing framework: Null (H0) and Alternative (H1) Hypothesis.
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 and Non-Parametric: ANOVA basics and Chi-square
Goodness-of-Fit tests.
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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.
Weightage: Continuous Assessment: 40%, End Semester Examinations:
60%
Mandated Activities with weightage: Assignments (10%), MATLAB
Activities (10%), Case study (10%), Tutorials* (), Quiz (10%)
Assessment Methodology: Assignments (20%), Solution to
application-oriented problems using software (20%), Solving competitive
examinations questions (20%), Internal Examinations (40%).
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