Course title: Probability & Statistics for Engineers
Lecture hours: 3
Tutorial hour(s): 1
Typical Slot: A
Description:
- Understand probabilistic modeling of uncertainty and randomness.
- Understand distributions, random variables and random process representations.
- Understand Bayesian and classical frameworks of inference.
- Perform conditioning, expectation, and correlation.
- Generate data from a probabilistic model.
- Learn and apply statistical techniques to infer model parameters from the data.
Course content:
- Probability Axioms of probability, independence, mutual exclusivity, conditioning, Bayes theorem.
- Random variables Discrete and continuous random variables, probability mass and density functions, transformation of random variables, expectations.
- Distributions Joint and marginal distributions, moment generating functions, characteristic functions, entropy, uniform, exponential, binomial, geometric, Gaussian, Poisson, beta, chi-square and Pareto distributions.
- Concentration inequalities Markov, Chebyshev, and Chernoff inequalities, law of large numbers, central limit theorem.
- Sampling Rejection sampling, acceptance sampling, Monte Carlo methods, bootstrapping, design of experiments.
- Statistical Inference Likelihood, posteriors, bias, maximum likelihood and maximum aposteriori estimation, conjugate prior, confidence interval, p-value, linear regression, hypothesis tests, naive Bayes classifier.
Prerequisite: None
Books:
- S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, 5th Ed., Elsevier.
- S.M. Ross, A First Course in Probability, 10th Ed., Pearson.
- A. Papoulis and S. Pillai, Probability – Random Variables and Stochastic Processes, 4th Ed., McGraw Hill.
- G. Casella and R. L. Berger, Statistical Inference, Cengage Learning.
Previous Instance of the course:
- 2025 (Jan-May; Dr. Ganapathy Krishnamurthi)